Harvard University signaled Friday that it would resist President Trump’s renewed threat to revoke the school’s tax-exempt status, a move for which it said there was “no legal basis” as the president escalated his bitter dispute with the nation’s oldest university.

Harvard stopped short of explicitly pledging a legal challenge to a revocation of its tax status, a change that would upend the university’s finances. But a spokesperson for the university said in a statement that there was “no legal basis to rescind Harvard’s tax-exempt status.”

“Such an unprecedented action would endanger our ability to carry out our educational mission,” the statement said. “It would result in diminished financial aid for students, abandonment of critical medical research programs and lost opportunities for innovation. The unlawful use of this instrument more broadly would have grave consequences for the future of higher education in America.”

Mr. Trump declared Friday morning on social media that the government would be “taking away Harvard’s Tax Exempt Status.” Mr. Trump added, “It’s what they deserve.”

Despite Mr. Trump’s assertion online and Harvard’s sharp response, it was not immediately clear Friday whether the I.R.S. was in fact moving forward with revoking Harvard’s tax-exempt status, a change that could typically occur only after a lengthy process. Federal law prohibits the president from directing the I.R.S. to conduct tax investigations, and I.R.S. employees who receive such a command are required to report it to an internal government watchdog.

After Mr. Trump first publicly called for Harvard to lose its tax exemption last month, White House officials said that the I.R.S. would make its own conclusion about whether to do so.

Representatives for the I.R.S. and Treasury Department, which oversees the tax collector, did not respond to a request for comment.

With its tax-exempt status, Harvard not only does not have to pay most taxes, but donors can write off gifts to the school on their own tax returns. Losing the status would not only force Harvard to start paying tax to the federal government on its income but could cause donations to dry up. Philanthropy accounts for about 45 percent of Harvard’s annual operating revenues; most of that sum comes from a payout from the university’s $53 billion endowment.

The intensifying standoff between the Trump administration and Harvard is part of a broad pressure campaign against some of the nation’s most elite universities, which the administration has painted as hotbeds of antisemitism and discrimination that require federal intervention.

In recent weeks, Harvard has taken a decidedly confrontational posture toward the Trump administration. The university rejected a roster of demands from the government, including that it submit reports to Washington, alter its admissions and hiring policies and bring in an outsider to examine “those programs and departments that most fuel antisemitic harassment or reflect ideological capture.”

The university sued after the administration froze more than $2 billion in federal funds in retaliation for Harvard’s defiance.

Even before Mr. Trump first called for Harvard to lose its tax exemption, the Trump administration has sought to transform the typically technocratic I.R.S. into a political tool.

Trump officials pressured the I.R.S. to help Immigration and Customs Enforcement find people it is seeking to deport, a decision that agency officials warned undermined legal protections for taxpayer information. (I.R.S. officials can face prison time if they improperly share taxpayer information, including details about whether an individual or entity is facing an audit.)

The agency has had five different leaders so far this year, with the current acting commissioner, Michael Faulkender, taking over after Treasury Secretary Scott Bessent complained to Mr. Trump that Elon Musk had installed the previous acting leader behind his back. Mr. Faulkender is also the deputy Treasury secretary.

Republicans have long accused the I.R.S. of improperly scrutinizing conservatives, leading a series of investigations under the Obama administration into the agency’s treatment of Tea Party groups. An inspector general later concluded that the agency had improperly targeted both conservative and liberal organizations.

“I think Republicans should be quite cautious about using the I.R.S. against any particular sector or narrow group of organizations,” said Scott Hodge, the former president of the Tax Foundation, a think tank that favors lower taxes. “Weaponizing the I.R.S. in any form is wrong. Policies should always be uniform and neutral and based on tax principles.”

A group of Democratic senators — led by Chuck Schumer of New York, the minority leader — wrote to the Treasury inspector general for tax administration, the I.R.S. watchdog, to request that it investigate Mr. Trump’s targeting of Harvard. They wrote that “it is both illegal and unconstitutional for the I.R.S. to take direction from the president” on assessing tax-exempt groups.

Typically, the I.R.S. will challenge a group’s tax-exempt status after conducting a lengthy audit to determine whether, for example, the entity is engaging in too much political or commercial activity. If the I.R.S. decides to revoke a tax exemption, the group can appeal the decision in court. Given Harvard’s vast research and educational operations, tax experts expect a court would ultimately side with the school.

“Been there, done that,” said Ted Mitchell, the president of the American Council on Education and an under secretary of education during the Obama administration. “The president has been saying this for weeks. Nothing has changed to make it possible for him to take unilateral action on an institution’s nonprofit status.”

Even if the I.R.S. does not ultimately change Harvard’s tax status, Republicans are preparing to substantially increase a tax on university endowments that the party created in 2017.