INVESTOR RIGHTS AGREEMENT

Exhibit 4.3

Execution Version

INVESTOR RIGHTS AGREEMENT

This Investor Rights Agreement (this “Agreement”) is entered into as of July 9, 2007 by and between Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”), and Jefferies & Company, Inc., (the “Investor” and, individually or with any subsequent holders of Registrable Securities, a “Holder”).

WHEREAS, pursuant to the Engagement Letter, dated May 4, 2007 as amended by Amendment to Engagement Letter dated June 18, 2007, as amended (the “Engagement Letter”), between the Company and the Investor, the Company has granted to the Investor a warrant (the “Warrants”) to purchase 550,000 shares of common stock, $0.0006 par value, of the Company (the “Common Stock”); and

WHEREAS, the Company has agreed to provide the registration rights set forth in this Agreement in connection with the Warrants;

NOW, THEREFORE, for and in consideration of the mutual covenants and conditions as set forth in the in the Engagement Letter, the Warrants and this Agreement, the parties hereto hereby agree as follows:

(a) Demand Registration Rights. Upon the written request of Holders of a majority of the Registrable Securities, the Company will use commercially reasonable efforts to promptly file and cause to become effective in accordance with Section 2 a Registration Statement under the Securities Act on such form as is appropriate covering the offer and sale from time to time, by the methods of distribution designated by the Holders to the Company in writing, such number of Registrable Securities as it has received written requests from Holders to include within such Registration Statement, which shall include a duly completed selling stockholder questionnaire in the form provided by the Company. Notwithstanding the foregoing and notwithstanding any provision of this Agreement to the contrary, the Company shall not be obligated to file and cause to become effective more than one (1) Registration Statement pursuant to this Section 1(a).

(b) Piggyback Registration Rights. In the event the Company intends to file a Registration Statement under the Securities Act (other than on Form S-4 or Form S-8 or any successor form for the registration of securities issued or to be issued in connection with a merger or acquisition or employee benefit plan) covering the offer and sale of Common Stock by the Company or by other selling shareholders, the Company shall give written notice thereof to the Holders, and the Company shall include in such registration such number of Registrable Securities for which it has received written requests (which shall include a duly completed selling stockholder questionnaire in the form provided by the Company) from Holders to include within such Registration Statement within fifteen (15) days after the Company has sent written notice to such Holders.

(c) Underwritten Offerings. If the Registration Statement under subsection (b) above is to cover an Underwritten Offering, the Registrable Securities shall be included in the underwriting on the same terms and conditions as the securities otherwise being sold through the underwriters. If, in the good faith judgment of the managing underwriter in any Underwritten Offering, the inclusion of all of the shares of Registrable Securities and any other Common Stock requested to be registered in such Underwritten Offering would interfere with the successful marketing of a smaller number of such shares, then the number of shares of Registrable Securities and other Common Stock to be included in the offering (except for shares to be issued by the Company in an offering initiated by the Company) shall be reduced to such smaller number as the managing underwriter shall in its sole discretion determine. The reduction in participation by Holders of Registrable Securities shall occur on a pro rata basis with all other participating holders of securities to be registered under such Registration Statement, except to the extent that certain holders of other securities may have a contractual preference to participate granted prior to the date hereof. In such case, the Company and the managing underwriter shall use their reasonable best efforts to accommodate the selling desires of the Holders of Registrable Securities and the Holders of other shares of Common Stock of the Company who possess such registration rights. Any shares for which the Company has received written request to register and are excluded from an Underwritten Offering as discussed above, shall be withheld from the market by the holders thereof for a period of time, not to exceed 30 days prior to the effective date and 90 days thereafter, that the managing underwriter reasonably determines is necessary in order to effect the Underwritten Offering.

If and whenever the Company is required to register Registrable Securities, the Company will use its reasonable best efforts to effect such registration to permit the sale of such Registrable Securities in accordance with the Holders, intended plan of distribution thereof (as communicated in writing to the Company), and pursuant thereto the Company will as expeditiously as possible:

(a) (i) (A) prepare and file with the SEC as soon as practicable (and in any event, subject to the last paragraph of this Section 2, within 45 days after any written request made pursuant to Section 1(a)) a Form S-3 Registration Statement, or a Form S-1 Registration Statement if the Company is not then eligible to use Form S-3 (or in the last case the successor form), with respect to such Registrable Securities and use its reasonable best efforts to cause such Registration Statement to become effective as soon as possible and remain continuously effective and (B) prepare and file with the SEC such amendments and post-effective amendments to the Registration Statement, and such supplements to the related prospectus, as may be reasonably requested by the Holders or any underwriter of Registrable Securities or as may be required by the rules, regulations or instructions applicable to the registration form used by the Company or by the Securities Act or rules and regulations thereunder to keep the Registration Statement effective, in the case of either foregoing clause (A) or foregoing clause (B), until all of the Registrable Securities covered by such Registration Statement have been sold under the Registration Statement or cease to be Registrable Securities, (ii) include in such Registration Statement and/or Prospectus (as the case may be) the names of the Holders who have delivered written notice, and a duly completed selling stockholder questionnaire (in the form provided by the Company) to the Company at least five business days prior to the date that

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the Registration Statement is first declared effective, that they propose to include Registrable Securities in the Registration Statement as selling securityholders, and (iii) file pursuant to Rule 424(b) under the Securities Act a supplement to the prospectus contained in the registration Statement or, if required, file a post-effective amendment to the Registration Statement, in each case, to cover new Holders of Registrable Securities upon at least seven business days prior written notice by such new Holders to such effect and the delivery by such new Holders of duly completed selling stockholder questionnaires (in the form provided by the Company).

(b) [reserved]

(c) deliver to the Holders and the underwriters, if any, without charge, as many copies of each prospectus (and each preliminary prospectus) and any amendments or supplements thereto as such Persons may reasonably request (the Company hereby consenting to the use of each such prospectus (or preliminary prospectus) by the Holders and the underwriters, if any, in connection with the offering and sale of the Registrable Securities covered by such prospectus (or preliminary prospectus).

(d) register or qualify or cooperate with the Holders, the underwriters, if any, and their respective counsel in connection with the registration or qualification of such Registrable Securities for offer and sale under the securities or blue sky laws of such jurisdictions as the Holders or underwriters may designate in writing and do anything else necessary or advisable to enable the disposition in such jurisdictions of the Registrable Securities covered by the Registration Statement; provided that the Company shall not be required to qualify generally to do business in any jurisdiction where it is not then so qualified or to take any action which would subject it to general service of process in any such jurisdiction where it is not then so subject.

(e) The Company shall give written notice to the Holders of the Registrable Securities included within the coverage of the Registration Statement (which notice pursuant to clauses (ii)-(v) hereof shall be accompanied by an instruction to suspend the use of the prospectus until the requisite changes have been made):

(i) when the Registration Statement or any amendment thereto has been filed with the SEC and when the Registration Statement or any post-effective amendment thereto has become effective;

(ii) of any request by the SEC for amendments or supplements to the Registration Statement or the prospectus included therein or for additional information;

(iii) of the issuance by the SEC of any stop order suspending the effectiveness of the Registration Statement or the initiation of any proceedings for that purpose;

(iv) of the receipt by the Company or its legal counsel of any notification with respect to the suspension of the qualification of the Securities for sale in any jurisdiction or the initiation or threatening of any proceeding for such purpose; and

(v) of the happening of any event that requires the Company to make changes in the Registration Statement or the prospectus in order that the Registration Statement or the prospectus do not contain an untrue statement of a material fact nor omit to state a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading.

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(f) The Company shall make every reasonable effort to obtain the withdrawal, at the earliest possible time, of any order suspending the effectiveness of the Registration Statement.

(g) The Company shall furnish to each Holder of Registrable Securities included within the coverage of the Registration Statement, without charge, if the Holder so requests in writing, at least one copy of the Registration Statement and any post-effective amendment thereto, including, but only if expressly requested by such Holder, financial statements and schedules and all exhibits thereto (including those, if any, incorporated by reference).

(h) The Company shall cooperate with the Holders of the Registrable Securities to facilitate the timely preparation and delivery of certificates (if any) representing the Registrable Securities to be sold pursuant to the Registration Statement free of any restrictive legends and in such denominations and registered in such names as the Holders may request a reasonable period of time prior to sales of the Registrable Securities pursuant to the Registration Statement.

(i) Upon the occurrence of any event contemplated by paragraphs (ii) through (v) of Section 2(e) above, the Company shall promptly prepare and file a post-effective amendment to the Registration Statement or a supplement to the related prospectus and any other required document so that, as thereafter delivered to Holders of the Registrable Securities or purchasers of Registrable Securities, the prospectus will not contain an untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading. If the Company notifies the Holders of Registrable Securities included within the coverage of the Registration Statement to suspend the use of the prospectus as a result of any of the events described in paragraphs (ii) through (v) of Section 2(e) above, until (A) the requisite changes to the prospectus have been made and the Holders have received copies of a supplemented or amended prospectus or (B) the Holders have been advised in writing by the Company that the use of the prospectus may be resumed, the Holders shall suspend use of such prospectus.

(j) The Company may require each Holder of Registrable Securities to be sold pursuant to the Registration Statement to furnish to the Company, pursuant to a questionnaire or otherwise, such information regarding the Holder and the distribution of the Registrable Securities as the Company may from time to time reasonably require for inclusion in the Registration Statement, and the Company may exclude from such registration the Registrable Securities of any Holder that fails to furnish such information within the applicable time period specified in this Agreement.

(k) In the case of any registration, the Company shall (i) make reasonably available for inspection by the Holders of the Registrable Securities, any underwriter participating in any disposition pursuant to the Registration Statement and any attorney, accountant or other agent retained by the Holders of the Registrable Securities or any such underwriter all relevant financial and other records, pertinent corporate documents and properties of the Company and (ii) cause the Company’s officers, directors, employees, accountants and auditors to supply all relevant information reasonably requested by the Holders of the Registrable Securities or any

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such underwriter, attorney, accountant or agent in connection with the Registration Statement, in each case, as shall be reasonably necessary to enable such persons, to conduct a reasonable investigation within the meaning of Section 11 of the Securities Act; provided, however, that the foregoing inspection and information gathering shall be coordinated on behalf of Holders by the Investor or by one counsel designated by the Holders.

(l) In the case of any registration, the Company, if requested by any Holder of Registrable Securities covered thereby in connection with an underwritten offering of the Registrable Securities pursuant to the Registration Statement, shall cause (i) its counsel (which may include the Company’s general counsel and/or the Company’s outside counsel) to deliver an opinion or opinions and updates thereto relating to the Registrable Securities in customary form addressed to the underwriters thereof and dated, in the case of the initial opinion, the effective date of such Registration Statement (it being agreed that the matters to be covered by such opinion shall include, without limitation, the due incorporation and good standing of the Company and its subsidiaries; the qualification of the Company and its subsidiaries to transact business as foreign corporations; the due authorization, execution and delivery of the relevant underwriting agreement; the due authorization, execution, authentication and issuance, and the validity and enforceability, of the Registrable Securities; the absence of material legal or governmental proceedings involving the Company and its subsidiaries; the absence of governmental approvals required to be obtained in connection with the Registration Statement, the offering and sale of the Registrable Securities; the compliance as to form of such Registration Statement and any documents incorporated by reference therein with the requirements of the Securities Act and the Exchange Act; and, as of the date of the opinion and as of the effective date of the Registration Statement or most recent post-effective amendment thereto, as the case may be, the absence from such Registration Statement and the prospectus included therein, as then amended or supplemented, and from any documents incorporated by reference therein of an untrue statement of a material fact or the omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading (in the case of any such documents, in the light of the circumstances existing at the time that such documents were filed with the Commission under the Exchange Act); (ii) its officers to execute and deliver all customary documents and certificates and updates thereof requested by any underwriters of the Registrable Securities and (iii) its independent public accountants to provide to the underwriter(s) of the Registrable Securities a comfort letter in customary form and covering matters of the type customarily covered in comfort letters in connection with primary underwritten offerings, subject to receipt of appropriate documentation as contemplated, and only if permitted, by Statement of Auditing Standards No. 72.

(m) The Company shall use its reasonable best efforts to cause the Common Stock included in such Registration Statement to be, upon resale thereunder, listed on each U.S. securities exchange or national quotation system, if any, on which any shares of Common Stock are then listed.

Notwithstanding the undertakings in this Section 2, in the event the Board of Directors of the Company in good faith determines that significant corporate developments preclude the filing of a Registration Statement or its being declared effective, the Company may delay the filing or effectiveness of such Registration Statement for a period not to exceed 30 days from the date of such request, after giving notice to any Holder of Registrable Securities to be covered by such Registration Statement.

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The Registration Expenses in connection with all registrations shall be borne by the Company, except that (i) the fees and disbursements of any counsel to the Holders shall be paid by such Holders if such Holders are unwilling to be represented by counsel to the Company, and (ii) the Holders shall pay all underwriting discounts or commissions, any selling commissions and stock transfer taxes attributable to sales of their Registrable Securities. The Company will bear its internal expenses (including, without limitation, all salaries and expenses of its officers and employees performing legal or accounting duties), the expenses of any annual audit and the fees and expenses of any person, including special experts, retained by the Company.

(a) The Company agrees to indemnify and hold harmless the Holders and each person, if any, who controls any Holder within the meaning of the Securities Act or the Exchange Act and the respective officers, directors, partners, employees, representatives and agents of such Holder or any controlling person of such Holder (the Holders and such persons are referred to as an “Indemnified Holder”) from and against any losses, claims, damages or liabilities, joint or several, or any actions in respect thereof (including, but not limited to, any losses, claims, damages, liabilities or actions relating to purchases and sales of the Securities) to which each Indemnified Holder may become subject under the Securities Act, the Exchange Act or otherwise, insofar as such losses, claims, damages, liabilities or actions arise out of or are based upon any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or prospectus or in any amendment or supplement thereto or in any preliminary prospectus relating to the Registration Statement or any other materials or information provided to investors by, or with the written approval of, the Company in connection with any offering pursuant to the Registration Statement, or arise out of, or are based upon, the omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading, and shall reimburse, as incurred, the Indemnified Holders for any legal or other expenses reasonably incurred by them in connection with investigating or defending any such loss, claim, damage, liability or action in respect thereof; provided, however, that the Company shall not be liable under this Section 4(a) in any such case to the extent that such loss, claim, damage or liability arises out of or is based upon any untrue statement or alleged untrue statement or omission or alleged omission made in the Registration Statement or prospectus or in any amendment or supplement thereto or in any preliminary prospectus relating to a registration in reliance upon and in conformity with written information pertaining to the Holder and furnished to the Company by or on behalf of the Holder specifically for inclusion therein. This indemnity agreement will be in addition to any liability which the Company may otherwise have to any Indemnified Holder. The Company shall notify each Indemnified Holder promptly of the institution, threat or assertion of any claim, proceeding (including any governmental investigation) or litigation in connection with the matters addressed by this Agreement that involves the Company or such Indemnified Holder.

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(b) Each of the Holders by its request for inclusion of Registrable Securities in any Registration Statement agrees, severally and not jointly, to indemnify and hold harmless the Company, its officers and directors and each person, if any, who controls the Company, its officers and directors within the meaning of the Securities Act or the Exchange Act from and against any losses, claims, damages or liabilities or any actions in respect thereof, to which the Company or any such person may become subject under the Securities Act, the Exchange Act or otherwise, insofar as such losses, claims, damages, liabilities or actions arise out of or are based upon any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or prospectus or in any amendment or supplement thereto or in any preliminary prospectus relating to the Registration Statement or any other materials or information provided to investors by, or with the written approval of, the Company in connection with any offering pursuant to the Registration Statement, or arise out of or are based upon the omission or alleged omission to state therein a material fact necessary to make the statements therein, in light of the circumstances under which they were made, not misleading, but in each case only to the extent that the untrue statement or omission or alleged untrue statement or omission was made in reliance upon and in conformity with written information pertaining to such Holder and furnished to the Company by or on behalf of such Holder specifically for inclusion therein. The liability of a Holder under this Section 4(b) shall in no event exceed the net proceeds received by such Holder from sales of Registrable Securities giving rise to such obligation.

(c) Promptly after receipt by a party of notice of the commencement of any action or proceeding (including a governmental investigation), such party (the “Indemnified Person”) will, if a claim in respect thereof is to be made against any party under this Section 4 (each an “Indemnifying Person”), notify the Indemnifying Person of the commencement thereof; but the omission so to notify the Indemnifying Person will not, in any event, relieve the Indemnifying Person from any obligations to any Indemnified Person (including the contribution provision hereof) that the Indemnifying Person may have under paragraph (a) or (b) above, except to the extent that the Indemnifying Person has been materially prejudiced (through the forfeiture of substantive rights or defenses) by such failure, or otherwise than under paragraph (a) or (b) above. In case any such action is brought against any Indemnified Person, and it notifies the Indemnifying Person of the commencement thereof, the Indemnifying Person will be entitled to participate therein and, to the extent that it may wish, jointly with any other Indemnifying Person similarly notified, to assume the defense thereof, with counsel reasonably satisfactory to such Indemnified Person (who shall not, except with the consent of the Indemnified Person, be counsel to the Indemnifying Person), and after notice from the Indemnifying Person to such Indemnified Person of its election so to assume the defense thereof the Indemnifying Person will not be liable to such Indemnified Person under this Section 4 for any legal fees, other than reasonable costs of investigation, subsequently incurred by such Indemnified Person in connection with the defense thereof. In any such proceeding, any Indemnified Person shall have the right to retain its own counsel at its own expense. Notwithstanding the foregoing, the Indemnifying Person shall pay as incurred (or within 30 days of presentation) the fees and expenses of the counsel retained by the Indemnified Person in the event (i) the Indemnifying Person and the Indemnified Person shall have mutually agreed to the retention of such counsel, (ii) the named parties to any such proceeding (including any impleaded parties) include both the Indemnifying Person and the Indemnified Person and representation of both parties by the same counsel would be inappropriate due to actual or potential differing interests between them or (iii)

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the Indemnifying Person shall have failed to assume the defense of and employ counsel reasonably acceptable to the Indemnified Person within a reasonable period of time after notice of commencement of the action. The Indemnifying Person shall not be liable for any settlement of any proceeding effected without its written consent, but if settled with such consent or if there be a final judgment for the plaintiff, the Indemnifying Person agrees to indemnify the Indemnified Person from and against any loss or liability by reason of such settlement or judgment. No Indemnifying Person shall, without the prior written consent of the Indemnified Person, effect any settlement of any pending or threatened action in respect of which any Indemnified Person is or could have been a party and indemnity could have been sought hereunder by such Indemnified Person unless such settlement (i) includes an unconditional release of such Indemnified Person from all liability on any claims that are the subject matter of such action, and (ii) does not include a statement as to or an admission of fault, culpability or a failure to act by or on behalf of any Indemnified Person.

(d) If the indemnification provided for in this Section 4 is unavailable or insufficient to hold harmless an Indemnified Person under subsections (a) or (b) above in respect of any losses, claims, damages or liabilities (or actions or proceedings in respect thereof) referred to therein, except by reason of the exceptions set forth in Section 4(a) or (b) or the failure of the Indemnified Person to give notice as required in Section 4(c), then each Indemnifying Person shall contribute to the amount paid or payable by such Indemnified Person as a result of the losses, claims, damages or liabilities (or actions in respect thereof) referred to in subsection (a) or (b) above in such proportion as is appropriate to reflect the relative fault of the Indemnifying Person or Persons on the one hand and the Indemnified Person on the other in connection with the statements or omissions that resulted in such losses, claims, damages or liabilities (or actions in respect thereof) as well as any other relevant equitable considerations. The relative fault of the parties shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to information supplied by the Company, on the one hand, or the Holder, on the other, and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission. The amount paid by an Indemnified Person as a result of the losses, claims, damages or liabilities referred to in the first sentence of this subsection (d) shall be deemed to include any legal or other expenses reasonably incurred by such Indemnified Person in connection with investigating or defending any action or claim which is the subject of this subsection (d). Notwithstanding any other provision of this Section 4(d), a Holder shall not be required to contribute any amount in excess of the amount by which the net proceeds received by such Holder from the sale of the Registrable Securities pursuant to the Registration Statement exceeds the amount of damages which the Holder would have otherwise been required to pay by reason of such untrue or alleged untrue statement or omission or alleged omission. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. For purposes of this paragraph (d), each person, if any, who controls such Indemnified Person within the meaning of the Securities Act or the Exchange Act shall have the same rights to contribution as such Indemnified Person and each person, if any, who controls the Company within the meaning of the Securities Act or the Exchange Act shall have the same rights to contribution as the Company.

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(e) The remedies provided by this Section 4 are not exclusive and shall not limit any rights or remedies that may otherwise be available to any indemnified party at law or in equity. The agreements contained in this Section 4 shall survive the sale of the Registrable Securities pursuant to the Registration Statement and shall remain in full force and effect, regardless of any termination or cancellation of this Agreement or any investigation made by or on behalf of any indemnified party.

If any of the Registrable Securities covered by any registration pursuant to Section 1(a) are to be sold in an Underwritten Offering, (a) the investment banker or investment bankers and manager or managers that will administer the offering will be selected by the Holders of a majority in number of such Registrable Securities to be included in such offering and (b) the Company shall, if requested, enter into an underwriting agreement in customary form in connection therewith. No person may participate in any Underwritten Offering pursuant to a registration initiated by the Company unless such person (a) agrees to sell such person’s Registrable Securities on the basis reasonably provided in any underwriting arrangements approved by the Company, which approval may not be withheld unreasonably, and (b) completes and executes all questionnaires, powers of attorney, indemnities, underwriting agreements and other documents required under the terms of such underwriting arrangements; provided, that the term of such underwriting arrangement in connection with the sale of Registrable Securities shall be no less favorable than the terms afforded to the Company or any other holder of securities participating in the Underwritten Offering.

The Company shall file the reports required to be filed by it under the Securities Act and the Exchange Act in a timely manner and, if at any time while there are outstanding securities that constitute Registrable Securities hereunder the Company is not required to file such reports, it will, upon the request of any Holders, make publicly available other information so long as necessary to permit sales of their Registrable Securities pursuant to Rule 144. The Company covenants that it will take such further action as any Holder may reasonably request, all to the extent required from time to time to enable such Holder to sell Registrable Securities without registration under the Securities Act within the limitation of the exemptions provided by Rule 144. Upon the written request of any Holder, the Company shall deliver to such Holder a written statement as to whether it is subject to and has complied with the reporting requirements referenced in the first sentence of this Section 6. Notwithstanding the foregoing, nothing in this Section 6 shall be deemed to require the Company to register any of its securities or to file periodic, current or other reports in each case pursuant to the Exchange Act.

(a) Counterparts. This Agreement may be executed through the use of separate signature pages or in any number of counterparts, and each of such counterparts shall, for all purposes, constitute one agreement binding on all the parties, notwithstanding that all parties are not signatories to the same counterpart.

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(b) Entire Agreement. This instrument contains the entire agreement of the parties, and there are no representations, covenants or other agreements except as stated or referred to herein.

(c) Preemptive Rights. For so long as any Warrants are outstanding, the Investor will be entitled to participate in any of the Company’s future offerings of Common Stock of the Company or securities of the Company convertible into, or exercisable for, Common Stock of the Company (as the case may be, “Additional Securities”) in which the aggregate offering price of such securities is equal to or exceeds $15 million.

Each time the Company proposes to offer any Additional Securities in which the aggregate offering price is equal to or exceeds $15 million, the Company shall make an offering of such Additional Securities to the Investor in accordance with the following provisions:

(i) The Company shall deliver a notice (the “Issuance Notice”) to the Investor stating (a) its bona fide intention to offer such Additional Securities, (b) the number of such Additional Securities to be offered, (c) the price and terms, if any, upon which it proposes to offer such Additional Securities, and (d) the anticipated closing date of the sale of such Additional Securities.

(ii) By written notification delivered to the Company within five trading days after the date of the Issuance Notice, the Investor may elect to purchase, at the price and on the terms specified in the Issuance Notice, Additional Securities equal to the number of Registrable Securities then held by the Investor (for purposes of clarification, in the event such Additional Securities are securities convertible into, or exercisable for, shares of the Common Stock of the Company, the number or amount of such Additional Securities which the Investor shall be entitled to purchase pursuant to this Section 7(c) shall be equal to the number or amount of such Additional Securities which are initially convertible into, or exercisable for, the number of shares of Common Stock of the Company equal to the number of Registrable Securities then held by the Investor).

The rights of the Investor under this Section 7(c) shall not apply to: (A) the exercise of any warrants, options or other convertible securities of the Company outstanding on the date hereof, (B) the issuance to employees and directors of Common Stock, stock awards or options under, or the exercise of any such options granted pursuant to, any employee stock option or similar employee incentive or benefit plan for the issuance of stock awards, options or capital stock of the Company approved by the Board of Directors, (C) the issuance of shares of Common Stock of the Company in connection with a bona-fide strategic transaction, partnership or acquisition or (D) the issuance of shares of Common Stock of the Company pursuant to a stock split, combination or subdivision of the outstanding shares of Common Stock or preferred stock (as the case may be) of the Company.

(d) Notices. All notices and other communications provided for or permitted hereunder shall be made in writing by hand delivery, registered first-class mail, facsimile transmission, or courier which guarantees overnight delivery:

Jefferies & Company, Inc.

520 Madison Avenue

New York, New York 10022

Attention: David Pritchard

Fax No.: (212)  ###-###-####

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with a copy (which shall not constitute notice) to:

Jefferies & Company, Inc.

520 Madison Avenue

New York, New York 10022

Attention: Ashley Geller

Fax No.: (212)  ###-###-####

Transmeridian Exploration Incorporated

397 N. Sam Houston Parkway E., Suite 300

Houston, Texas 77060

Attention: Nicolas J. Evanoff

Fax No.: (281)  ###-###-####

with a copy (which shall not constitute notice) to:

Akin Gump Strauss Hauer & Feld LLP

1111 Louisiana Street, 44th Floor

Houston, Texas 77002

Attention: James L. Rice III

Fax No.: (713)  ###-###-####

All such notices and communications shall be deemed to have been duly given: at the time delivered by hand, if personally delivered; the earlier of the date indicated on the notice of receipt and five business days after being deposited in the mail, postage prepaid, if mailed; when receipt is acknowledged by recipient’s facsimile machine operator, if sent by facsimile transmission during normal business hours; and on the day delivered, if sent by overnight air courier guaranteeing next day delivery.

(e) Successors and Assigns. This Agreement shall inure to the benefit of and be binding upon the successors and assigns of each of the parties, including, without the need for an express assignment or any consent by the Company thereto, subsequent holders of the Warrants or Registrable Securities. The Company hereby agrees to extend the benefits of this Agreement to any holder of the Warrants or Registrable Securities and any such holder may specifically enforce the provisions of this Agreement as if an original party hereto.

(f) Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY, AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS WITHOUT REGARD TO THE PROVISIONS THEREOF RELATING TO CONFLICTS OF LAWS. THE COMPANY HERETO IRREVOCABLY CONSENTS TO THE NON-EXCLUSIVE

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JURISDICTION OF THE STATE AND FEDERAL COURTS LOCATED IN HOUSTON, TEXAS IN CONNECTION WITH ANY ACTION OR PROCEEDING ARISING OUT OF OR RELATING TO THIS AGREEMENT. IN ANY SUCH LITIGATION THE COMPANY AGREES THAT THE SERVICE THEREOF MAY BE MADE BY CERTIFIED OR REGISTERED MAIL DIRECTED TO THE COMPANY PURSUANT TO SECTION 7(d).

(g) Remedies. The Company acknowledges and agrees that any failure by the Company to comply with its obligations under Section 1 hereof may result in material injury to the Holders for which there is no adequate remedy at law, that it will not be possible to measure damages for such injuries precisely and that, in the event of any such failure, any Holder may obtain such relief as may be required to specifically enforce the Company’s obligations under Section 1 hereof. The Company further agrees to waive the defense in any action for specific performance that a remedy at law would be adequate.

(h) No Inconsistent Agreements. The Company will not on or after the date of this Agreement enter into any agreement with respect to its securities that is inconsistent with the rights granted to the Holders in this Agreement or otherwise conflicts with the provisions hereof. The rights granted to the Holders hereunder do not in any way conflict with and are not inconsistent with the rights granted to the holders of the Company’s securities under any agreement in effect on the date hereof.

(i) Amendments and Waivers. The provisions of this Agreement may not be amended, modified or supplemented, and waivers or consents to departures from the provisions hereof may not be given, except by the Company and the written consent of the Holders of a majority in number of the Restricted Securities affected by such amendment, modification, supplement, waivers or consents, provided, however, that without the consent of each Holder of the Restricted Securities, the provisions of Section 4 of this Agreement may not be amended, modified or supplemented and waivers or consents to departures from the provisions therefrom may not be given. Each Holder of Registrable Securities outstanding at the time of any amendment, modification, supplement, waiver, or consent or thereafter shall be bound by any such amendment, modification, supplement, waiver, or consent effected pursuant to this Section 7(i), whether or not any notice of such amendment, modification, supplement, waiver, or consent is delivered to such Holder.

Exchange Act: The Securities Exchange Act of 1934, as from time to time amended.

Registration Expenses: Registration Expenses shall mean:

(1) all registration and filing fees (including fees with respect to filings required to be made with the SEC and the National Association of Securities Dealers, Inc.);

(2) fees and expenses of compliance with securities or blue sky laws (including fees and disbursements of counsel for the underwriters in connection with blue sky qualifications of the Registrable Securities) and all application and filing fees in connection with listing on a national securities exchange or automated quotation system pursuant to the requirements hereof;

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(3) printing, messenger, telephone and delivery expenses;

(4) fees and disbursements of counsel for the Company; and

(5) fees and disbursements of all independent certified public accountants of the Company (including the expenses of any special audit and comfort letters required by or incident to such performance).

Registration Expenses shall not include: (i) the fees and disbursements of any counsel to the Holders, which shall be paid by such Holders if such security Holders are unwilling to be represented by counsel to the Company, and (ii) any underwriting discounts or commissions, any selling commissions and stock transfer taxes attributable to sales of Registrable Securities.

Registrable Securities: (a) the shares of Common Stock of the Company or other securities issued or issuable upon exercise of the Warrants (b) any securities issued or issuable with respect to such Common Stock or other securities by way of a stock dividend or stock split or in connection with a combination of shares, recapitalization, merger, consolidation or reorganization and (c) any Additional Securities issued to the Investor pursuant to Section 7(c) of this Agreement; provided, however, that any such securities shall be deemed to be Registrable Securities only if and so long as they are Transfer Restricted Securities.

Registration Statement: With respect to Section 1(a), a registration statement which covers Registrable Securities pursuant to the provisions of this Agreement, and with respect to Section 1(b), any other form of registration statement that the Company determines, in its sole discretion to file, and in each case including the related prospectus included in such registration statement, amendments (including post-effective amendments) and supplements to such registration statement, and all exhibits to and all material incorporated by reference in such registration statement.

SEC: The Securities and Exchange Commission.

Securities Act: The Securities Act of 1933, as from time to time amended.

Transfer Restricted Security: A security that has not been sold to or through a broker, dealer or underwriter in a public distribution or other public securities transaction or sold in a transaction exempt from the registration and prospectus delivery requirements of the Securities Act under Rule 144(k) promulgated thereunder (or any successor rule other than proposed Rule 144A). The foregoing notwithstanding, a security shall remain a Transfer Restricted Security until (i) all stop transfer instructions or notations and restrictive legends with respect to such security are eligible to be removed and (ii) the Holder has received an opinion of counsel to the Company, to the effect that such shares in the Holder’s hands are freely transferable in any public or private transaction without registration under the Securities Act (or such Holder has waived receipt of such opinion).

Underwritten Registration or Underwritten Offering: A registration or offering in which securities of the Company are sold to an underwriter for distribution to the public.

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This Agreement is effective as of the date first written above.

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Investor Rights Agreement dated as of July 9, 2007