US President Donald Trump on Wednesday announced a ban on visas for foreign students who are set to begin attending Harvard University, ramping up his administration's crackdown on higher education.

"I have determined that it is necessary to restrict the entry of foreign nationals who seek to enter the United States solely or principally to participate in a course of study at Harvard University or in an exchange visitor program hosted by Harvard University," Trump said in a statement late Wednesday.

The Trump administration has been in an ongoing showdown with academia, and Harvard in particular.

The Ivy League institution has continually drawn Trump's ire while publicly rejecting his administration's repeated demands to give up control of recruitment, curricula and research choices.

Trump's proclamation said his decision would take effect immediately and "shall apply to aliens who enter or attempt to enter the United States to begin attending Harvard University" through the Student and Exchange Visitor Program.

It added that current international students already attending Harvard on various visas faced a review, and risked having "their visas revoked."

The move was necessary to protect "national security," the statement said.

"In my judgement, it presents an unacceptable risk to our Nation's security for an academic institution to refuse to provide sufficient information, when asked, about known instances of misconduct and criminality committed by its foreign students," Trump said.

He also charged that "Harvard and its affiliated organizations on campus continue to deny hardworking Americans equal opportunities."

"It is not in the interest of the United States to further compound Harvard's discrimination against non-preferred races, national origins, shared ancestries, or religions by further reducing opportunities for American students through excessive foreign student enrollment," it said.

Wednesday's edict appears to apply to Harvard University only.

The Trump administration has targeted foreign students explicitly, with Secretary of State Marco Rubio vowing to "aggressively" revoke visas to students from China.

Last week, as students graduated, a judge extended a temporary block on Trump's bid to prevent Harvard from enrolling international students.