Harvard University said on Monday that it had rejected policy changes requested by the Trump administration, becoming the first university to directly refuse to comply with the administration’s demands and setting up a showdown between the federal government and the nation’s wealthiest university.

Other universities have pushed back against the Trump administration’s interference in higher education. But Harvard’s response, which essentially called the Trump administration’s demands illegal, marked a major shift in tone for the nation’s most influential school, which has been criticized in recent weeks for capitulating to Trump administration pressure.

A letter the Trump administration sent to Harvard on Friday demanded that the university reduce the power of students and faculty members over the university’s affairs; report foreign students who commit conduct violations immediately to federal authorities; and bring in an outside party to ensure that each academic department is “viewpoint diverse,” among other steps. The administration did not define what it meant by viewpoint diversity, but it has generally referred to seeking a range of political views, including conservative perspectives.

“No government — regardless of which party is in power — should dictate what private universities can teach, whom they can admit and hire, and which areas of study and inquiry they can pursue,” said Alan Garber, Harvard’s president, in a statement to the university on Monday.

Since taking office in January, the Trump administration has aggressively targeted universities, saying it is investigating dozens of schools as it moves to eradicate diversity efforts and what it says is rampant antisemitism on campus. Officials have suspended hundreds of millions of dollars in federal funds for research at universities across the country.

The administration has taken a particular interest in a short list of the nation’s most prominent schools. Officials have discussed toppling a high-profile university as part of their campaign to remake higher education. They took aim first at Columbia University, then at other members of the Ivy League, including Harvard.

Harvard, for its part, has been under intense pressure from its own students and faculty to be more forceful in resisting the Trump administration’s encroachment on the university and on higher education more broadly.

The Trump administration said in March that it was examining about $256 million in federal contracts for Harvard, and an additional $8.7 billion in what it described as “multiyear grant commitments.” The announcement went on to suggest that Harvard had not done enough to curb antisemitism on campus. At the time, it was vague about what the university could do to satisfy Trump administration concerns.

Last month, more than 800 faculty members at Harvard signed a letter urging the university to “mount a coordinated opposition to these anti-democratic attacks.”

The university appeared to take a step in that direction on Monday. In his letter rejecting the administration’s demands, Dr. Garber suggested that Harvard had little alternative.

“The university will not surrender its independence or relinquish its constitutional rights,” he wrote. “Neither Harvard nor any other private university can allow itself to be taken over by the federal government.”

The government’s letter to Harvard on Friday demanded an extraordinary set of changes that would have reshaped the university and ceded an unprecedented degree of control over Harvard’s operations to the federal government. The changes would have violated principles that are held dear on colleges campuses, including academic freedom.

Some of the actions that the Trump administration demanded of Harvard were:

• Sharing all its hiring data with the Trump administration, and subjecting itself to audits of its hiring while “reforms are being implemented,” at least through 2028.

• Providing all admissions data to the federal government, including information on both rejected and admitted applicants, sorted by race, national origin, grade-point average and performance on standardized tests.

• Immediately shutting down any programming related to diversity, equity and inclusion.

• Overhauling academic programs that the Trump administration says have “egregious records on antisemitism,” including placing certain departments and programs under an external audit. The list includes the Divinity School, the Graduate School of Education, the School of Public Health and the Medical School, among many others.

“Harvard has in recent years failed to live up to both the intellectual and civil rights conditions that justify federal investment,” the Trump administration letter said.

Last month, after the Trump administration stripped $400 million in federal funds from Columbia University, Columbia agreed to major concessions demanded by the federal government. It agreed to place its Middle Eastern studies department under different oversight and to create a new security force of 36 “special officers” empowered to arrest and remove people from campus.

The demands on Harvard were different, and much more expansive, touching on many aspects of the university’s basic operations.

In Harvard’s response on Monday, it said it had already made major changes over the last 15 months to improve its campus climate and counter antisemitism, including disciplining students who violate university policies, devoting resources to programs that promote ideological diversity, and improving security.

Harvard said it was unfortunate that the administration had ignored the university’s efforts and moved instead to infringe on the school’s freedom in unlawful ways.

The forceful posture taken by Harvard on Monday was applauded across higher education, after universities had drawn widespread criticism for failing to resist Mr. Trump’s attacks more aggressively.

Harvard itself had been under fire for a series of moves in recent months that faculty members said were taken to placate Mr. Trump, including hiring a lobbying firm with close ties to the president and pushing out the faculty leaders of the Center for Middle Eastern Studies.

A Harvard faculty group filed a lawsuit last week, seeking to block the administration from carrying out its threat to withdraw federal funding from the university. Nikolas Bowie, a law professor and secretary-treasurer of Harvard’s chapter of the American Association of University Professors, the group that filed the suit, applauded Harvard’s rejection of the Trump administration’s demands.

“I’m grateful for President Garber’s courage and leadership,” said Dr. Bowie. “His response recognizes that there’s no negotiating with extortion.”

Ted Mitchell, president of the American Council on Education, which represents many colleges and universities in Washington, said Harvard’s approach could embolden other campus leaders, whom he said were “breathing a sigh of relief.”

“This gives more room for others to stand up, in part because if Harvard hadn’t, it would have said to everyone else, ‘You don’t stand a chance,’” said Dr. Mitchell, a former president of Occidental College. “This gives people a sense of the possible.”

He described Harvard’s response as “a road map for how institutions could oppose the administration on this incursion into institutional decision-making.” He added, “Whether it’s antisemitism or doing merit-based hiring or merit-based admissions, the basic texture of the academic enterprise needs to be decided by the university, not by the government.”

Ethan Kelly, 22, a senior at Harvard from Maryland, said that Monday’s message from Dr. Garber was a relief. He said that he and many of his classmates have been concerned that their school would cave to the Trump administration’s demands.

“There’s been so much concern that Harvard would fold under political pressure, especially with how aggressive the Trump administration has been in trying to control higher education,” Mr. Kelly said. Seeing Dr. Garber draw a clear line, he added, was something “that matters.”

Stephanie Saul, Alan Blinder and Miles Herszenhorn contributed reporting.