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.