EXHIBIT 32.1

CERTIFICATIONS OF

CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER

OF TVARDI THERAPEUTICS, INC.

PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906 OF THE

SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Tvardi Therapeutics, Inc. (the "Company") for the quarter ended March 31, 2025, as filed with the Securities and Exchange Commission on the date hereof (the "Report"), Imran Alibhai, Chief Executive Officer of the Company, and Dan Conn, Chief Financial Officer of the Company, each hereby certifies, pursuant to the requirement set forth in Rule 13a-14(b) of the Securities Exchange Act of 1934, as amended, (the “Exchange Act”) and Section 1350 of Chapter 63 of Title 18 of the United States Code (18 U.S.C. §1350), that, to the best of his knowledge, based upon a review of the Report:

(1)

The Report fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act; 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/ IMRAN ALIBHAI
Name: Imran Alibhai
Title: Chief Executive Officer (Principal Executive Officer)
Date: May 13, 2025


/s/ DAN CONN
Name: Dan Conn
Title: Chief Financial Officer (Principal Financial Officer)
Date: May 13, 2025

This certification accompanies the Form 10-Q to which it relates, is not deemed filed with the Securities and Exchange Commission and is not to be incorporated by reference into any filing of Tvardi Therapeutics, Inc. under the Securities Act of 1933, as amended, or the Securities Exchange Act of 1934, as amended (whether made before or after the date of the Form 10-Q), irrespective of any general incorporation language contained in such filing.