The Trump administration on Monday sought to force Harvard University back to the negotiating table by informing the nation’s oldest and wealthiest college that it would not be eligible for any new federal grants.

That decision was relayed in a contentious letter to Alan M. Garber, the president of Harvard, from Linda McMahon, the education secretary, who blasted the school for “disastrous mismanagement.”

“This letter is to inform you that Harvard should no longer seek grants from the federal government, since none will be provided,” Ms. McMahon wrote in the letter.

It was the first significant response from the administration since Harvard sued to challenge the government’s decision to cut billions of dollars in research funding after the university defied demands for intrusive oversight.

An Education Department official who briefed reporters about the letter before it was released said that Harvard’s eligibility for research grants depended on its ability to first address concerns about antisemitism on campus, policies that consider a student’s race, and complaints from the administration that the university has abandoned its pursuit of “academic excellence” while employing relatively few conservative faculty members.

In a statement on Monday night, a Harvard spokesperson said the letter showed the administration “doubling down on demands that would impose unprecedented and improper control over Harvard University and would have chilling implications for higher education.”