The Internal Revenue Service is weighing whether to revoke Harvard’s tax exemption, according to three people familiar with the matter, which would be a significant escalation of the Trump administration’s attempts to choke off federal money and support for the leading research university.

President Trump on Tuesday publicly called for Harvard to pay taxes, continuing a standoff in which the administration has demanded the university revamp its hiring and admissions practices and its curriculum.

Some I.R.S. officials have told colleagues that the Treasury Department on Wednesday asked the agency to consider revoking Harvard’s tax-exempt status, according to two of the people, who spoke on the condition of anonymity to describe internal conversations.

An I.R.S. spokeswoman declined to comment. The Treasury Department did not respond to a request for comment. CNN first reported that the I.R.S. was looking at potentially rescinding Harvard’s tax-exempt status.

Federal law bars the president from either directly or indirectly requesting the I.R.S. to investigate or audit specific targets. The I.R.S. does at times revoke tax exemptions from organizations for conducting too many political or commercial activities, but those groups can appeal the agency’s decision in court. Any attempt to take away Harvard’s tax exemption would be likely to face a legal challenge, which tax experts expect would be successful.

Harrison Fields, a White House spokesman, said the I.R.S.’s scrutiny of Harvard began before the president’s social media post.

“Any forthcoming actions by the I.R.S. are conducted independently of the President, and investigations into any institution’s violations of their tax status were initiated prior to the President’s TRUTH,” Mr. Fields said in a statement, referring to Mr. Trump’s website Truth Social.

In a statement, Harvard said there is no legal basis for rescinding its tax status.

“Such an unprecedented action would endanger our ability to carry out our educational mission,” the university 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.”

Even an attempt at changing Harvard’s tax status would signify a drastic breach in the independence of the I.R.S. and its historical insulation from political pressure.

The Trump administration has cleared out much of the agency’s senior leadership in the last few months, installing allies to temporarily serve as the commissioner and its top lawyer. Its newest acting commissioner, Gary Shapley, was an I.R.S. agent who has said that the investigation into the taxes of Hunter Biden, former President Joseph R. Biden Jr.’s son, was not aggressive enough.

Not only does Harvard’s tax-exempt status allow it to forgo paying income and property taxes, but it also means that donations to the university are tax deductible. That helps attract huge donations from ultrawealthy Americans.

The university is already under intense financial pressure. The Trump administration has said it is cutting off $2.2 billion in federal funding for Harvard after it refused to comply with a list of the government’s demands.

On Wednesday, the homeland security secretary, Kristi Noem, canceled nearly $3 million in agency grants to Harvard, according to a statement from the Department of Homeland Security.

Ms. Noem also wrote a letter to university officials requesting “detailed records on Harvard’s foreign student visa holders’ illegal and violent activities” by the end of the month, according to the agency statement. Without a response, the university could lose the “privilege of enrolling foreign students,” the statement said.

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. Led by top White House aides and senior officials from agencies across the government, the effort is part of a bid by conservatives to realign the liberal tilt of academia.

The strategy has roiled higher education as the Trump administration scrutinizes dozens of schools over their handling of antisemitism allegations, diversity practices and policies on transgender athletes. At stake are billions of dollars in federal funding that the White House is threatening to pull from universities that do not comply.

In recent weeks, Harvard has had to weigh whether to rely on its endowment of $53 billion, the largest in higher education, to withstand backlash from the federal government.

But the bulk of its endowment is “restricted,” or earmarked for causes specified by donors. Universities are loath to use even the free parts of their endowments — about $10 billion in Harvard’s case — viewing them more like retirement accounts they rely on for yearly operating expenses than rainy-day funds.