Transmeridian Exploration (TMYEQ) 10-K 2005 FY Annual report

Exhibit 32.1

Certification of Chief Executive Officer pursuant to 18 U.S.C. Section 1350, as adopted pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

March 16, 2006

Securities and Exchange Commission

450 Fifth Street, N.W.

Washington, D.C. 20549

Re: Certification Required Under Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the accompanying report on Form 10-K for the period ended December 31, 2005, and filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Lorrie T. Olivier, President and Chief Executive Officer of Transmeridian Exploration Incorporated (the “Company”), hereby certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Lorrie T. Olivier

Lorrie T. Olivier

President and Chief Executive Officer