Columbia University agreed on Friday to overhaul its protest policies, security practices and Middle Eastern studies department in a remarkable concession to the Trump administration, which has refused to consider restoring $400 million in federal funds without major changes.

The agreement, which stunned and dismayed many members of the faculty, could signal a new stage in the administration’s escalating clash with elite colleges and universities. Harvard, Stanford, the University of Michigan and dozens of other schools face federal inquiries and fear similar penalties, and college administrators have said Columbia’s response to the White House’s demands may set a dangerous precedent.

This week, the University of Pennsylvania was also explicitly targeted by the Trump administration, which said it would cancel $175 million in federal funding, at least partly because the university had let a transgender woman participate on a women’s swim team.

Columbia, facing the loss of government grants and contracts over what the administration said was a systemic failure to protect students and faculty members “from antisemitic violence and harassment,” opted to yield to many of the administration’s most substantial demands.

The university said it had agreed to hire a new internal security force of 36 “special officers” who will be empowered to remove people from campus or arrest them. The wearing of face masks on campus will also be banned for the purpose of concealing identity during disruptions, with exceptions for religious and health reasons.

Columbia will also adopt a formal definition of antisemitism, something many universities have shied away from even as they, like Columbia, faced pressure to do so amid protests on their campuses over the war in Gaza. Under the working definition, antisemitism could include “targeting Jews or Israelis for violence or celebrating violence against them” or “certain double standards applied to Israel,” among other issues.

Taken together, the administration’s plan — issued in an unsigned, four-page letter — reflected a stunning level of deference to the Trump administration from a top private research university.

Columbia’s interim president, Katrina A. Armstrong, said in a separate letter that the university’s actions were part of its effort to “make every student, faculty and staff member safe and welcome on our campus.”

“The way Columbia and Columbians have been portrayed is hard to reckon with,” Dr. Armstrong said. “We have challenges, yes, but they do not define us.”

She added: “At all times, we are guided by our values, putting academic freedom, free expression, open inquiry, and respect for all at the fore of every decision we make.”

The Trump administration demanded each of the changes in a letter to Columbia officials on March 13. It was not immediately clear whether the university’s actions would be sufficient to reclaim the $400 million in federal money. A spokeswoman for the Education Department, one of three federal agencies named in the letter, did not immediately respond on Friday to a request for comment, including to questions about the potential restoration of federal funding.

In perhaps the most contentious move, Columbia said it would appoint a senior vice provost to oversee the Middle Eastern, South Asian and African Studies Department. The White House had demanded that the department be placed under academic receivership, a rare federal intervention in an internal process that is typically reserved as a last resort in response to extended periods of dysfunction.

Columbia did not refer to the move related to the Middle Eastern studies department as receivership, but several faculty members said that it appeared to resemble that measure.

Legal scholars and advocates for academic freedom expressed alarm on Friday over what they described as Columbia’s dangerous surrender to President Trump at a perilous moment for higher education. Some critics of the university’s response said they feared the White House could target any recipient of federal funds, including K-12 public schools, hospitals, nursing homes and business initiatives.

Sheldon Pollock, a retired former chair of the university’s Middle Eastern studies department, said in a text message that “Columbia faculty are utterly shocked and profoundly disappointed by the trustees’ capitulation to the extortionate behavior of the federal government.”

“This is a shameful day in the history of Columbia,” Dr. Pollock said, adding that it would “endanger academic freedom, faculty governance and the excellence of the American university system.”

The moves by Columbia were first reported by The Wall Street Journal.

The school’s response to the administration’s demands was the latest turn in a turbulent phase that began 17 months ago, when pro-Israel and pro-Palestinian students organized competing protests in the days after the Hamas-led Oct. 7, 2023, attack on Israel.

Since then, the Manhattan campus has experienced a rare summoning of the police to quell protests, the president’s resignation and the detention of Mahmoud Khalil, a recent graduate, by federal immigration officials.

The extraordinary cancellation of funding for the university escalated the crisis, imperiling research that includes dozens of medical and scientific studies. (The university did not mention the loss of funds in outlining the steps it was taking.)

On social media, Jameel Jaffer, the director of the Knight First Amendment Institute at Columbia, called it “a sad day for Columbia and for our democracy.”

Others said that a wholesale overhaul was appropriate in light of the conflict and tension on campus in recent semesters.

Ester R. Fuchs, who co-chairs the university’s antisemitism task force, said that many of the administration’s changes appeared to be issues that the group had previously highlighted.

“What’s fascinating to me is a lot of these are things we needed to get done and were getting done, but now we’ve gotten done more quickly,” said Dr. Fuchs, who is also a professor of international and public affairs and political science.

She added: “We are completely supportive of principles of academic freedom.”

Among other changes, the university also said that the administration would work to adopt a universitywide “position of institutional neutrality.” It said that it would move an independent panel of faculty, students and staff members who handle disciplinary procedures under the provost’s office — and that members would be “restricted to faculty and administrators only.”

The school also agreed to review its admissions policies for potential bias after it “identified a recent downturn in both Jewish and African American enrollment,” and last week announced a range of disciplinary actions against an undisclosed number of students.

Despite the overhaul, the current fraught chapter in Columbia’s 270-year history may not be over. The Trump administration has told the university that meeting its demands was “a precondition for formal negotiations” over a continued financial relationship and that the White House may call for other “immediate and long-term structural reforms.”

Columbia’s changes are notable for their scope and for how quickly they were made. But it is not the only institution to make concessions as the White House indicates that its campaign against elite universities and colleges will not end at the Morningside Heights campus.

Federal money is the lifeblood of major research universities, and some have begun to keep quiet on hot-button issues in hopes of escaping the administration’s ire. Many, including the University of California this week, have retreated from diversity-related efforts.

Many of the changes Columbia agreed to make involve issues that have been points of contention on campus for some time.

Face masks, for example, emerged as a source of conflict last year amid the Gaza protests, with demonstrators saying they should be able to conceal their identities to avoid being doxxed, and others arguing that mask-wearing makes it harder to hold protesters accountable if their actions veer into harassment.

The detainment this month of Mr. Khalil, a prominent figure in the protests who stood out because he chose not to wear a mask, cast a spotlight on the issue.

But putting the Middle Eastern studies department, which has long been in a pitched battle over its scholarship and the employment of professors who describe themselves as anti-Zionist, under outside scrutiny provoked unique outrage.

Columbia said that the senior vice provost would review curriculum and hiring in several programs, including the Center for Palestine Studies and the Institute for Israel and Jewish Studies. The university said the move was aimed at “promoting excellence in regional studies.”

But Michael Thaddeus, a Columbia math professor who described reading Dr. Armstrong’s letter with “profound disappointment and alarm,” called it “a giant step down a very dangerous road.”

He worried that the Middle Eastern studies department would effectively be run by “a member of Columbia’s thought police” who could interfere with anything from course offerings to faculty appointments. “It strikes at the heart of academic freedom,” Professor Thaddeus said.

“Of all the bad things,” he continued, “this one is really the worst.”

Katherine Rosman contributed reporting.