PURCHASE AGREEMENT

Exhibit 10.7

Execution Copy

PURCHASE AGREEMENT

THIS PURCHASE AGREEMENT (“Agreement”) is made as of the 12 day of December, 2005, by and between TRANSMERIDIAN EXPLORATION, INC., a company organized in the British Virgin Islands with registered offices at Quastisky Building, 3^rd Floor, P.O. Box 905, Road Town, Tortola (the “Company”), and KORNERSTONE INVESTMENT GROUP LTD., a company organized in the British Virgin Islands with registered offices at Trident Chambers, P.O. Box 146, Wickhams Cay, Road Town, Tortola (“Kornerstone”).

RECITALS

WHEREAS, the Company and Kornerstone entered into that certain Consultancy Agreement dated May 1, 1999 (the “Consultancy Agreement”), whereby the Company retained the services of Kornerstone to support the Company in legal and tax research, contract drafting and discussions with third parties including the Government of Kazakhstan on various matters as provided for therein;

WHEREAS, under the terms of such Consultancy Agreement, as compensation for such services, the Company assigned to Kornerstone a carried working interest equal to ten percent (10%) of the Company’s interest in the South Alibek License 1557 (as more particularly described in the Consultancy Agreement, the “Working Interest”).

WHEREAS, Kornerstone has entered into a consulting agreement with the Company’s affiliate JSC Caspi Neft TME in Kazakhstan, and the Company and Kornerstone desire to cancel and terminate the Consultancy Agreement effective upon the closing of the Company’s agreement to purchase Bramex Management, Inc. on or before December 23, 2005 (the “Effective Date”); and

WHEREAS, in consideration of such cancellation of the Consultancy Agreement by the Company, Kornerstone is conveying, assigning, and transferring to the Company all of Kornerstone’s right, title and interest in and to the Working Interest on the Effective Date, all under and subject to the terms and conditions of this Agreement;

NOW THEREFORE, in consideration of the mutual covenants and agreements contained herein, the parties hereby agree as follows:

1. Cancellation and Termination of the Consultancy Agreement; Conveyance of Working Interest. The Company and Kornerstone hereby terminate and cancel, effective upon the Effective Date, the Consultancy Agreement and any amendments thereto, and all of the obligations of the parties thereunder are effectively terminated (other than sections 4.1 and 6.1 of the Consultancy Agreement, which shall survive such termination) at such time. In consideration thereof (and for the further consideration set forth herein below), and in reliance on the representations and warranties, and upon the terms and subject to the conditions of this Agreement, on the Effective Date Kornerstone is hereby selling, assigning, conveying, transferring, and delivering to the Company, and the Company is hereby purchasing, all of Kornerstone’s right, title and interest in and to the Working Interest, free and clear of all liens, claims, charges, restrictions, equities, or encumbrances of any kind. As further consideration for such sale, assignment,

conveyance and transfer of the Working Interest, the Company and Kornerstone hereby agree as follows:

a. The Company shall pay to Kornerstone cash consideration in the amount of U.S. Fifteen Million Two Hundred Fifty Thoursand Dollars (US$15,250,000.00), payable on the Effective Date. Such amount shall be payable by wire transfer or other payment method as mutually agreeable to the parties hereto;

b. The Company shall cause Transmeridian Exploration Incorporated, a Delaware corporation and the parent corporation of the Company (“TMI”), to issue to Kornerstone an aggregate amount of One Million (1,000,000) shares of TMI’s Common Stock, $0.0006 par value, equivalent in value to U.S. Four Million Dollars (US$3,750,000) based upon a price of $3.75 per share (the “TMI Stock”); and

c. The TMI Stock is being issued pursuant to applicable exemptions from the registration requirements of the U.S. Securities Act of 1933 (the “Securities Act”), and thus are subject to the applicable resale restrictions and holding periods under such law.

2. Deliveries by Kornerstone. In exchange for the consideration set out above, Kornerstone is hereby delivering to the Company all of its right, title, and interests in and to the Working Interest, free and clear of all liens, claims, charges, restrictions, equities or encumbrances of any kind, effective upon the Effective Date. Kornerstone shall execute and deliver any and all documents, instruments, and other agreements (including without limitation, any and all documents and instruments that may need to be filed in Kazakhstan), and shall take any and all other action as may be necessary to effectively transfer and deliver the Working Interest to the Company and vest all right, title and interest in and to the Working Interest in the Company. Kornerstone shall cooperate at its expense with the Company, both before and after the date hereof, to the extent Company may reasonably request, in the defense of any proceeding seeking to restrain, prohibit or invalidate the transactions contemplated by this Agreement.

3. Representations and Warranties of Kornerstone.

a. Kornerstone has the power and authority to execute, deliver and perform this Agreement and all other instruments and documents required or contemplated to be executed, delivered and performed by it under this Agreement. Such execution, delivery and performance (i) have been duly authorized by all necessary corporate action by Kornerstone, (ii) do not and will not require the approval of any person whose approval has not been obtained, (iii) do not and will not contravene the organizational documents of Kornerstone, (iv) do not and will not contravene, conflict with, result in a violation (or any occurrence which by notice or passage of time or both would constitute a violation) of, or entitle any party to terminate, accelerate or declare a default with respect to, any contract, mortgage, franchise, deed of trust, lease, license or agreement of Kornerstone, or any rule, regulation, order, writ or decree applicable to Kornerstone, (v) do not and will not result in the creation or imposition of any lien, charge, encumbrance or claim of any nature whatsoever upon Working Interest, and (vi) will not result in the violation of any laws. This Agreement and each of the documents and instruments to be executed by Kornerstone and delivered

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to the Company pursuant to this Agreement when so delivered will constitute their respective legal, valid and binding obligations enforceable in accordance with each such Agreement’s, document’s, and instrument’s respective terms.

b. Kornerstone has good and marketable title to the Working Interest, has not assigned any right, title or interest in and to the Working Interest, and on the Closing the Working Interest will be free and clear of liens, claims, charges, mortgages, security interests, pledges, and encumbrances. Upon consummation of the transactions contemplated hereby, the Company shall receive good, valid and marketable title to the Working Interest.

c. There is no action, suit, proceeding, investigation or claim pending, or to Kornerstone’s best knowledge, threatened in law, equity or otherwise before any court, administrative agency or arbitrator which either (a) questions the validity of this Agreement, or (b) might adversely affect the right, title or interest of Kornerstone in the Working Interest.

d. Kornerstone acknowledges its understanding that the issuance of the TMI Stock is intended to be exempt from registration under the Securities Act and, in furtherance thereof, Kornerstone represents and warrants to and agrees with the Company that: (i) Kornerstone has the financial ability to bear the economic risk of its investment; (ii) Kornerstone certifies that it is not a U.S. person and is not acquiring the TMI Stock for the account or benefit of any U.S. person; (iii) Kornerstone agrees that it will hold the TMI Stock for investment purposes only and that any resale of such securities will be made strictly in accordance with the provisions of Regulation S promulgated under the Securities Act of 1933, pursuant to registration under the Securities Act, or pursuant to an available exemption from registration; and agrees not to engage in hedging transactions with regard to such securities unless in compliance with the Securities Act.

e. None of the representations and warranties made by Kornerstone, or made in any certificate or memorandum furnished or to be furnished by Kornerstone, on any of its behalf, contain or will contain any untrue statement of material fact, or omit any material fact, the omission of which would be misleading. All representations and warranties of the Kornerstone contained in this Agreement, or contained in any instrument, certificate, opinion or other document delivered by any of them, or on its behalf, pursuant to this Agreement, shall survive the execution of this Agreement, and Kornerstone shall indemnify, defend and hold harmless the Company and each of the Company’s parent, subsidiary, and affiliates from and against any and all claims, costs, and expenses arising out of any breach of any covenant or representation or warranty of Kornerstone under this Agreement.

4. Representations and Warranties of the Company.

a. The Company has the power and authority to execute, deliver and perform this Agreement and all other instruments and documents required or contemplated to be executed, delivered and performed by it under this Agreement. Such execution, delivery and performance (i) have been duly authorized by all necessary corporate action by the Company, (ii) do not and will not require the approval of any person whose approval has not been obtained, (iii) do not and will not contravene the organizational documents of the Company, (iv) do not and will not contravene,

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conflict with, result in a violation (or any occurrence which by notice or passage of time or both would constitute a violation) of, or entitle any party to terminate, accelerate or declare a default with respect to, any contract, mortgage, franchise, deed of trust, lease, license or agreement of the Company, or any rule, regulation, order, writ or decree applicable to Kornerstone, and (vi) will not result in the violation of any laws. This Agreement and each of the documents and instruments to be executed by the Company and delivered to Kornerstone pursuant to this Agreement when so delivered will constitute their respective legal, valid and binding obligations enforceable in accordance with each such Agreement’s, document’s, and instrument’s respective terms.

b. None of the representations and warranties made by Company, or made in any certificate or memorandum furnished or to be furnished by Company, on any of its behalf, contain or will contain any untrue statement of material fact, or omit any material fact, the omission of which would be misleading. All representations and warranties of the Company contained in this Agreement, or contained in any instrument, certificate, opinion or other document delivered by any of them, or on its behalf, pursuant to this Agreement, shall survive the execution of this Agreement, and the Company shall indemnify, defend and hold harmless Kornerstone from and against any and all claims, costs, and expenses arising out of any breach of any covenant or representation or warranty of the Company under this Agreement.

5. Restrictive Legends. Each certificate for the TMI Stock, and each certificate issued to any subsequent transferee of any such certificate, unless, in each case, such TMI Stock is eligible for resale without registration pursuant to Rule 144(k) under the Securities Act or such TMI Stock is being sold pursuant to an effective registration statement under the Securities Act, shall be stamped or otherwise imprinted with legends in substantially the following form:

“THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 AS AMENDED, AND MAY NOT BE OFFERED, SOLD, ASSIGNED OR TRANSFERRED, IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER SAID ACT OR UNLESS THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE COMPANY THAT REGISTRATION UNDER SAID ACT IS NOT REQUIRED.”

6. Registration Rights. The resale of the TMI Stock shall be registered in accordance with the terms and conditions contained in that certain Registration Rights Agreement executed by TMI and attached hereto as Exhibit A (the “Registration Rights Agreement”). Kornerstone acknowledges that pursuant to the Registration Rights Agreement, TMI has the right to request that Kornerstone furnish information regarding Kornerstone and the distribution of the TMI Stock as is required by law or the U.S. Securities Exchange Commission to be disclosed in the Registration Statement (as such term is defined in the Registration Rights Agreement), and TMI may exclude from such registration the shares of TMI Stock if Kornerstone fails to furnish such information within a reasonable time prior to the filing of each Registration Statement, supplemented prospectus included therein and/or amended Registration Statement.

7. Expenses. Each party hereto shall bear all of its own expenses in connection with the transactions contemplated herewith.

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8. Applicable Law. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH ENGLISH LAW.

9. Entire Agreement. This Agreement embodies the entire agreement and understanding of the parties hereto and supersedes any prior agreement or understanding between the parties.

10. Counterparts. This Agreement may be executed in several counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same document.

11. Binding Effect; Benefits. This Agreement shall inure to the benefit of and be binding upon the parties hereto and their respective heirs, administrators, executors, successors and assigns; provided, however, that nothing in this Agreement, expressed or implied, is intended to confer on any person other than the parties hereto or their respective heirs, successors and assigns, any rights and remedies, obligations or liabilities under or by reason of this Agreement.

12. Arbitration of Disputes. The parties agree that any future dispute, claim or controversy arising between them relating to or arising under this Agreement, whether based upon contract or tort, at law or in equity, shall be determined by arbitration in accordance with the arbitration rules established by the London Court of International Arbitration, with the arbitration taking place in London, England. The award of the arbitrator will be final and binding between the parties. The losing party will pay for the reasonable costs and legal fees of the other side incurred in reference to the arbitration. All proceedings will be conducted in the English language, and English law shall apply.

13. Confidentiality. Each of the parties agrees that he will maintain the confidentiality of this Agreement (except to the extent that disclosure is necessary to employees, agents, representatives, consultants or subcontractors of the Company in connection with the performance of the terms of this Agreement), and, in that connection, each agrees that he will not take any action intended to cause public disclosure of the terms of this Agreement, unless, in the good faith judgment of such party, such disclosure of this Agreement is required by law or is necessary in connection with endeavoring to enforce or require performance or observance of any of the terms or provisions of this Agreement or in connection with defending against any claim or any person against such party or in connection with endeavoring to protect or preserve the interests of such party or any right, title, property or interest herein provided to be granted or afforded to such party.

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IN WITNESS WHEREOF, each of the parties hereto has executed this Agreement as of the date first above written.

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Exhibit “A”

Registration Rights Agreement

This Registration Rights Agreement (“Agreement”) is entered into as of December __, 2005 by and between Transmeridian Exploration Incorporated, a Delaware corporation (the “Company”) and Kornerstone Investment Group Ltd. (the “Investor”). In order to induce the Investor to enter into that certain Purchase Agreement (herein so called) by and between Transmeridian Exploration, Inc., a wholly-owned subsidiary of the Company, and the Investor dated of even date herewith, the Company has agreed to provide the registration rights set forth in this Agreement. The effectiveness of this Agreement is conditioned upon the consummation of the closing of such Purchase Agreement.

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

1) Registration Rights

(a) 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 Investor, and the Company shall include in such registration such number of Registrable Securities for which it has received written requests from the Investor to include within such Registration Statement within fifteen (15) days after the Company has sent written notice to such Investor.

(b) Underwritten Offerings. If for any reason the Form S-3 Registration Statement under Subsection (a) above is to cover an Underwritten Offering, such 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. In this event, 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 Form S-3 Registration Statement or other Registration Statement (as applicable), except to the extent that certain holders of other securities may have a contractual preference to participate. 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 such shares and which are excluded from an underwritten public 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 180 days thereafter, that the managing underwriter reasonably determines is necessary in order to effect the underwritten public offering.

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2) Termination

If the Investor participates in an offering but ultimately decides not to sell upon the effectiveness of the Registration Statement including such shares, the obligations of the Company under this Registration Rights Agreement shall cease. In any event, this Registration Rights Agreement shall immediately terminate without further action on the part of the Company at such time as the securities that have registration rights under this Agreement shall no longer be Transfer Restricted Securities.

3) Registration Procedures

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 intended plan of distribution thereof, and pursuant thereto the Company will as expeditiously as possible:

(a) prepare and file with the SEC as soon as practicable a Form S-3 Registration Statement with respect to such Registrable Securities and use its best efforts to cause such Registration Statement to become effective and remain effective until the Registrable Securities covered by such Registration Statement have been sold, provided, however, in no event shall the Company be required to maintain the effectiveness of the Form S-3 Registration Statement for longer than one hundred eighty (180) days;

(b) prepare and file with the SEC such amendments and post-effective amendments to the Registration Statement, and such supplements to the Prospectus, as may be reasonably requested by the Investor 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 until all Registrable Securities covered by such Registration Statement are sold in accordance with the intended plan of distribution set forth in such Registration Statement or supplement to the Prospectus;

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

(d) register or qualify or cooperate with the Investor, 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 Investor or underwriters may designate in writing and do anything else necessary or advisable to enable the

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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.

Notwithstanding the undertakings in this Section 3, the Company may decline to file a Registration Statement after giving notice to any holder of Registrable Securities as discussed in Section 1, or withdraw a Registration Statement after filing and after such notice, but prior to the effectiveness thereof, provided, that the Company shall promptly notify each holder in writing of any such action and provided, further, that the Company shall bear all expenses which would otherwise have been charged to the holder in connection with such withdrawn Registration Statement. In taking such action, the Company shall have no liability to the holders of Registrable Securities to the extent it did not have a contractual requirement to file such Registration Statement or obtain its effectiveness.

4) Registration Expenses

The Registration Expenses of all Registrations shall be borne by the Company, except that (i) the fees and disbursements of any counsel to the selling security holders shall be paid by such holders if such security holders are unwilling to be represented by counsel to the Company, and (ii) the selling security holders shall pay all underwriting discounts or commissions, any selling commissions and stock transfer taxes attributable to sales of Registrable Securities.

5) Requirements for Participation in Underwritten Offerings

No person may participate in any Underwritten Offering pursuant to a Registration initiated by the Company hereunder unless such Person (a) agrees to sell such Person’s securities on the basis provided in any underwriting arrangements approved by the Company 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 any other holder of securities participating in the Underwritten Offering.

6) Suspension of Sales

Upon receipt of written notice from the Company that a Registration Statement or Prospectus contains a Misstatement, each Holder of Registrable Securities shall forthwith discontinue disposition of Registrable Securities until such Holder has received copies of a supplemented or amended Prospectus, or until such Holder is advised in writing by the Company that the use of the Prospectus may be resumed, and, if so directed by the Company, such Holder shall deliver to the Company (at the Company’s expense) all copies, other than permanent file copies then in such Holder’s possession, of the Prospectus covering such Registrable Securities current at the time of receipt of such notice.

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7) Miscellaneous

Any notice, demand or other communication which any party hereto may be required, or may elect, to give to anyone interested hereunder shall be sufficiently given if (a) deposited, postage prepaid, in a United States mail letter box, registered or certified mail, return receipt requested, addressed to such address as may be given herein, or (b) delivered personally at such address. 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. Except as otherwise provided herein, this Agreement shall be binding upon and inure to the benefit of the parties and their heirs, executors, administrators, successors, legal representatives and assigns. If the Investor is more than one person, the obligation of the Investor shall be joint and several and the agreements, representations, warranties and acknowledgments herein contained shall be deemed to be made by and be binding upon each such person and its heirs, executors, administrators and successors. 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. This Agreement is not transferable or assignable by the Investor. This Agreement shall be governed by and construed in accordance with the laws of the State of Texas.

8) Definitions

Registration Expenses: Registration Expenses shall mean:

(1) all registration and filing fees (including fees with respect to filings required to be made with the Securities and Exchange Commission 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);

(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 incurred specifically in connection with such Registration.

Registration Expenses shall not include: (i) the fees and disbursements of any counsel to the selling security 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) One Million (1,000,000) shares of Common Stock, $0.0006 par

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value, of the Company (the “TMI Stock”) issued to the Investor under the Purchase Agreement, and (b) any securities issued or issuable with respect to such TMI Stock by way of a stock dividend or stock split or in connection with a combination of shares, recapitalization, merger, consolidation or reorganization; provided, however, that any such shares or securities shall be deemed to be Registrable Securities only if and so long as it is a Transfer Restricted Security.

Registration Statement: Any other form of registration statement that the Company determines, in its sole discretion to file, and in each case including the 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.

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

SEC: The Securities and Exchange Commission.

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 of such security has received an opinion of counsel to the Company, to the effect that such shares in such 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 in which securities of the Company are sold to an underwriter for distribution to the public.

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IN WITNESS WHEREOF, each of the parties hereto has executed this Agreement as of the date first above written.

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