M.I.T.’s president acknowledged Thursday that he had signed a letter thanking Jeffrey Epstein for a donation in 2012 and said senior members of his administration had approved gifts from the disgraced financier as long as they remained anonymous.

Separately Thursday, the LinkedIn founder Reid Hoffman confirmed that he had helped raise funds from Mr. Epstein on behalf of the M.I.T. Media Lab and its director, Joichi Ito, a longtime friend.

The president, L. Rafael Reif, made his disclosure in an email to the university community less than a week after news of the anonymous donations contributed to the resignation of Mr. Ito, the director of M.I.T.’s prominent Media Lab. Mr. Ito stepped down after published reports described how the Media Lab had handled millions of dollars in gifts from or apparently facilitated by Mr. Epstein, who killed himself last month while awaiting trial in a Manhattan jail on federal sex-trafficking charges.

Mr. Reif said he did not remember signing the thank-you to Mr. Epstein in 2012, four years after Mr. Epstein pleaded guilty to a sex charge involving a minor in Florida and the year before Mr. Ito has said he met Mr. Epstein. “I apparently signed this letter on August 16, 2012, about six weeks into my presidency,” he said. “Although I do not recall it, it does bear my signature.”