EXHIBIT 32.1

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CERTIFICATION PURSUANT TO

18 U.S.C. § 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

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In connection with the Quarterly Report on Form 10-Q of Cellectar Biosciences, Inc. (the “Company”) for the quarter ended June 30, 2021, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, James V. Caruso, President and Chief Executive Officer of the Company, and Dov Elefant, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, to our knowledge, that:

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

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

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