Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002,

18 U.S.C. SECTION 1350

In connection with the Quarterly Report on Form 10-Q of Tamboran Resources Corporation (the “Company”) for the quarter ended December 31, 2025, as filed with the U.S. Securities and Exchange Commission on the date hereof (the “Report”), I, Todd Abbott, Chief Executive Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that, to my knowledge:

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

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

Date: February 11, 2026

/s/ Todd Abbott

Todd Abbott

Chief Executive Officer

(Principal Executive Officer)