Harvard says it won't take $8.6 million in coronavirus relief funding after all, a day after coming under fire from President Trump.

A reporter asked Mr. Trump at Tuesday's White House briefing if he was going to request that big companies return money they received through the government's small-business loan program, as Shake Shack had announced it would do. The president instead brought up Harvard, which had an endowment of $40.9 billion last year.

"Harvard's going to pay back the money," Trump said. "They shouldn't be taking it. I'm not going to mention any other names, but when I saw Harvard — they have one of the largest endowments anywhere in the country, maybe in the world, I guess. They're going to pay back that money."

President Trump says he will ask some major organizations to return relief money from the Paycheck Protection Program, specifically mentioning Harvard University https://t.co/9T8aUPjUrs pic.twitter.com/5C488zMdtK — CBS News (@CBSNews) April 21, 2020

However, Harvard disputed Mr. Trump's assertion. The university said it did not apply for the government's Paycheck Protection Program for small businesses — nor did it receive any funds through that program.

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"President Trump is right that it would not have been appropriate for our institution to receive funds that were designated for struggling small businesses," the school tweeted. "Like most colleges and universities, Harvard has been allocated funds as part of the CARES Act Higher Education Emergency Relief Fund."

The Higher Education Emergency Relief Fund makes up about $14 billion of the $2.2 trillion stimulus package signed by Mr. Trump last month. Harvard initially said it planned to use all of the nearly $9 million it received to "provide direct assistance to students facing urgent financial needs due to the COVID-19 pandemic."

However, on Wednesday, the university announced a reversal. In a statement, the university said it was "concerned ... that the intense focus by politicians and others on Harvard in connection with this program may undermine participation in a relief effort that Congress created and the President signed into law for the purpose of helping students and institutions whose financial challenges in the coming months may be most severe."

It continued, "As a result of this, and the evolving guidance being issued around use of the Higher Education Emergency Relief Fund, Harvard has decided not to seek or accept the funds allocated to it by statute."

The statement adds that the school "remains fully committed to providing the financial support that it has promised to its students."

Stanford, another top-tier American university with a high endowment, also said it will not take the funds. Stanford said it contacted the Department of Education to ask for its application for relief funds to be "rescinded."

Therefore, Monday morning we contacted the Department of Education to ask that our application for relief funds under the Higher Education Emergency Relief Fund section of the CARES act be rescinded.(5/6) — Stanford University (@Stanford) April 22, 2020

Princeton said it will "not accept" funding under the CARES Act. "Princeton has not yet received any of these funds, and never requested any of these funds," the school said on Twitter.

#PrincetonU has determined it will not accept funding allocated under the CARES Act. Princeton has not yet received any of these funds, and never requested any of these funds. pic.twitter.com/En4nhqyqkc — Princeton University (@Princeton) April 22, 2020

Meanwhile, many in higher education fear that the unprecedented combination of difficulties presented by the coronavirus pandemic could sound a death knell for many colleges throughout the United States.

"Families will have less money. Many of them won't have jobs for a while. You know, if they're relying on investments, they'll have less investments," said Dr. Thomas Bailey, president of Teachers College, Columbia University.

Editor's note: This story has been updated throughout with Harvard's decision to decline the federal funds.