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 annual report of Tamboran Resources Corporation (the “Company”) on Form 10-K for the year ended June 30, 2024 as filed with the U.S. Securities and Exchange Commission on the date hereof (the “Report”), I, Joel Riddle, 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:

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

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

Date: September 20, 2024