Harvard has been a central target in the White House’s campaign to stamp out what it calls “woke” and “radical left” ideologies on American campuses.
In April last year, Trump revoked around $2bn in research grants to Harvard and froze federal funding.
The university sued the Trump administration over the move, saying no government “should dictate what private universities can teach, whom they can admit and hire, and which areas of study and inquiry they can pursue”.
A US federal court later overturned the billions in funding cuts, ruling the government had violated university’s free speech rights.
The White House vowed to immediately challenge the “egregious decision”, saying Harvard remains “ineligible for grants in the future”.
Before Monday’s announcement, the government had been in discussions with Harvard over a potential deal to unfreeze federal funding.
“We are now seeking One Billion Dollars in damages, and want nothing further to do, into the future, with Harvard University,” Trump wrote on Monday.
He accused Harvard of “serious and heinous illegalities”, but did not clarify how he believed it had broken the law.
Trump has previously threatened to revoke Harvard’s tax-exempt status and take control of the university’s patents stemming from federally funded research.
Three other Ivy League universities, Columbia, Penn and Brown, struck deals with Trump to preserve funding that was at risk due to similar claims by the administration, rather than go to court.