The Trump administration warned 60 universities on Monday that they could face penalties from pending investigations into antisemitism on college campuses, a threat sharpened in recent days by its cancellation of funding to Columbia University and the arrest of a protest leader there.

The list of five dozen schools included colleges from both Republican- and Democratic-voting states, elite Ivy League schools such as Brown and Yale, state schools including Arizona State University and the University of Tennessee, and smaller institutions, like Muhlenberg College in Allentown, Pa., which has about 2,000 students.

President Trump seized on accusations of antisemitism as a cudgel against Democrats during his presidential campaign and has continued to prioritize the issue from the White House. Mr. Trump’s push comes as college campuses are embroiled in debates over what, precisely, constitutes antisemitism and whether that definition should include protests against Israel — even as many of the protesters themselves are Jewish.

Last week, Mr. Trump threatened to strip funding from schools that allow “illegal protests,” but did not elaborate on what he meant by that phrase.

His administration has also canceled $400 million in federal funding for Columbia University for what it said was “inaction in the face of persistent harassment of Jewish students.” The Trump administration has not said whether that decision was based on a particular finding from any of the three investigations into religious discrimination that were opened during the last 14 months of the Biden administration.

Instead, Mr. Trump’s new antisemitism task force notified Columbia on March 3 about a “comprehensive review” of the school’s federal contracts and grants. The administration announced that it was pulling $400 million from the school four days later.

The administration also invoked an obscure legal statute to arrest and try to deport a recent Columbia graduate who led protests there, though a federal judge in Manhattan ordered him not to be removed from the United States for now.

During a confirmation hearing last month for Linda McMahon, Mr. Trump’s education secretary, Senator Bill Cassidy of Louisiana, the Republican chairman of the Senate Education Committee, pressed Ms. McMahon about how she would direct the department to address its “backlog” of antisemitism investigations.

At the time, Ms. McMahon told Mr. Cassidy that she needed to learn more about the issue. On Friday, four days after her confirmation, the department announced that it would prioritize the resolution of antisemitism investigations.

According to department records, there were active investigations into religious discrimination at 40 of the 60 college campuses when Mr. Trump assumed office. At the time, nearly all of those cases were less than 14 months old.

An online database of existing federal investigations into colleges and universities has not been updated since Mr. Trump took office in January, and an Education Department spokesman said he was unable to provide information beyond the agency’s news release.

Ms. McMahon said in a statement on Monday that federal funding was a privilege for colleges and contingent on “scrupulous adherence” to anti-discrimination laws.

“The department is deeply disappointed that Jewish students studying on elite U.S. campuses continue to fear for their safety amid the relentless antisemitic eruptions that have severely disrupted campus life for more than a year,” Ms. McMahon said.