EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statements on Form S-8 (Registration Nos. 333-168252, 333-152250 and 333-111386) of RegeneRx Biopharmaceuticals, Inc. (the “Company”) of our report dated March 31, 2015, on our audits of the financial statements of RegeneRx Biopharmaceuticals, Inc. (which report expresses an unqualified opinion and includes an explanatory paragraph relating to the existence of substantial doubt about the Company’s ability to continue as a going concern) as of December 31, 2014 and 2013 and for the years then ended, which report is included in this Annual Report (Form 10-K) for the year ended December 31, 2014.

/s/ CohnReznick LLP

Vienna, Virginia

March 31, 2015