Harvard and MIT asked a court Wednesday to block an order by President Donald Trump's administration threatening the visas of foreign students whose entire courses have moved online because of the coronavirus pandemic.

The universities' lawsuit was in response to an announcement Monday by the US Immigration and Custom Enforcement (ICE) that the affected students must leave the country or transfer to a school offering in-person tuition.

"We will pursue this case vigorously so that our international students, and international students at institutions across the country, can continue their studies without the threat of deportation," Harvard President Lawrence Bacow said in a statement.

ICE said in its announcement the State Department would not issue visas to students enrolled in programs that are fully online for the fall semester and such students would not be allowed to enter the country.

Universities with a hybrid system of in-person and online classes will have to show that foreign students are taking as many in-person classes as possible, to maintain their status. The measure was seen as a move by the White House to put pressure on educational institutions that are adopting a cautious approach to reopening amid the global COVID-19 pandemic.

"The order came down without notice -- its cruelty surpassed only by its recklessness," Bacow said. "It appears that it was designed purposefully to place pressure on colleges and universities to open their on-campus classrooms for in-person instruction this fall, without regard to concerns for the health and safety of students, instructors and others," he added.

The universities say in their lawsuit that the order would harm students "immensely," both personally and financially. It describes the order as "arbitrary and capricious."

The plaintiffs ask that the court issue a temporary restraining order and "permanent injunctive relief" preventing the policy being enforced. They also ask that the order be declared unlawful, that their fees are covered, and that they receive any other relief that the court deems appropriate.

The lawsuit, filed in a Massachusetts district court, lists the defendants as ICE and the United States Department of Homeland Security. Most US colleges and universities have not yet announced their plans for the fall semester but Harvard University has said all its classes for the 2020-21 academic year will be conducted online "with rare exceptions."

It says packed classrooms would endanger the health of students and teachers. Trump has branded the decision "ridiculous."