Exhibit 13.1

CERTIFICATION OF THE CHIEF EXECUTIVE OFFICER PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906 OF THE U.S. SARBANES-OXLEY ACT OF 2002

In connection with the annual report of Icon Energy Corp. (the “Company”) on Form 20-F for the year ended December 31, 2024, as filed with the Securities and Exchange Commission (the “SEC”) on or about the date hereof (the “Report”), I, Ismini Panagiotidi, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 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 as of, and for, the periods presented in the Report.

The foregoing certification is provided solely for the purposes of complying with the provisions of Section 906 of the Sarbanes-Oxley Act of 2002 and is not intended to be used or relied upon for any other purpose.

A signed original of this written statement has been provided to the Company and will be retained by the Company and furnished to the SEC or its staff upon request.

Date: April 25, 2025

/s/ Ismini Panagiotidi

Ismini Panagiotidi

Chief Executive Officer (Principal Executive Officer)