A letter from Linda McMahon, the education secretary, said university leaders must demonstrate more responsible management before receiving additional federal grants.

President Trump on Friday said he would be “taking away” the university’s status, renewing a threat he made last month. It was not immediately clear if the I.R.S. was moving forward with a change.

The administration has accused the university of lacking viewpoint diversity. Harvard is fighting its demands, but embracing the vague term.

Alan Garber became a hero to liberals after Harvard resisted the federal government. At the same time, he is trying to remake campus culture in ways the Trump administration might appreciate.

Harvard has hired lawyers connected to conservative Supreme Court justices and President Trump himself to fight its case against the government.

The Trump administration on Thursday accused Harvard University of failing to report large foreign donations to the federal government as required by law, part of a widening effort to target the institution after it refused to comply with President …