Harvard University said it plans to keep an $8.6 million grant it received as part of a stimulus package to blunt the economic impact of the coronavirus lockdown, contradicting President Donald Trump who pledged Tuesday that the Ivy League university would return it.

Speaking at a press briefing on Tuesday, Trump pointed to the institution's ample endowment -- worth nearly $41 billion -- as the reason why it should hand over the money.

"Harvard is going to pay back the money and they shouldn't be taking it," Trump said, adding that Harvard has one of the largest endowments "in the country, maybe in the world."

In a statement issued moments after the briefing ended, however, Harvard said it planned "to direct 100% of the funds to financial assistance to students, and will not be using any of the funds to cover institutional costs."

The university said it received the grant through the educational relief program that was part of the $2.3 trillion stimulus passed at the end of March, which also included a much larger fund aimed at helping small businesses.

That fund has been riddled with controversy, including an outcry over disclosures that larger companies received bailout funds while many small businesses, among the hardest hit by the coronavirus crisis, still await aid. That fund was exhausted last week.

As U.S. states issued sweeping stay-at-home orders to slow the spread of the highly infectious coronavirus, businesses have shuttered and 22 million Americans have filed for unemployment.

On Monday, hamburger chain Shake Shack Inc said it would return the small business loan it received from the government, the first major firm to hand back money.

On Tuesday, Treasury Secretary Steve Mnuchin said "very clear guidelines" would be released to clarify what companies are eligible for the stimulus funds.

"The intent [of the program] was not for companies that have access to plenty of liquidity and other sources," he said. "To the extent these companies didn't understand this and they repay the loans, that will be OK. And, if not, there will be potentially other consequence," he said.

More aid may be coming soon. The Senate on Tuesday approved $484 billion in fresh relief for businesses and hospitals hammered by the coronavirus pandemic, sending the measure to the House of Representatives for final passage later this week.