A judge temporarily suspended on Friday the Trump administration's move to block Harvard from enrolling and hosting foreign students after the prestigious university sued, calling the action unconstitutional.

On Thursday, Homeland Security Secretary Kristi Noem revoked Harvard University's ability to enrol foreign nationals, throwing the future of thousands of students and the lucrative income stream they provide into doubt.

But Harvard sued, and Massachusetts district judge Allison Burroughs ordered that "The Trump administration is hereby enjoined from implementing... the revocation of Plaintiff's SEVP (Student and Exchange Visitor Programme) certification."

There will be an injunction hearing on May 29, a court filing showed.

US President Donald Trump is furious at Harvard – which has produced 162 Nobel prize winners – for rejecting his demand that it submit to oversight on admissions and hiring over his claims that it is a hotbed of anti-Semitism and "woke" liberal ideology.

His administration has already threatened to put US$9 billion of government funding to Harvard under review, gone on to freeze a first tranche of US$2.2 billion of grants and US$60 million of official contracts, as well as targeting a Harvard Medical School researcher for deportation.

"It is the latest act by the government in clear retaliation for Harvard exercising its First Amendment rights to reject the government's demands to control Harvard's governance, curriculum, and the 'ideology' of its faculty and students," said the lawsuit filed in Massachusetts federal court.

The lawsuit called for a judge to "stop the government's arbitrary, capricious, unlawful, and unconstitutional action."

The loss of foreign nationals – more than a quarter of its student body – could prove costly to Harvard, which charges tens of thousands of US dollars a year in tuition. (AFP)