Harvard University and the Massachusetts Institute of Technology filed a federal lawsuit Wednesday challenging the Trump administration's decision to bar international students from staying in the US if they take classes entirely online this autumn.

The lawsuit, filed in Boston's federal court, seeks to prevent federal immigration authorities from enforcing the rule. The universities contend that the directive violates the Administrative Procedures Act because officials failed to offer a reasonable basis justifying the policy and because the public was not given notice to comment on it.

The Trump administration did not immediately respond to requests for comment.

US Immigration and Customs Enforcement notified colleges on Monday that international students will be forced to leave the US or transfer to another college if their schools operate entirely online this fall. New visas will not be issued to students at those schools, and others at universities offering a mix of online and in-person classes will be barred from taking all of their classes online.

The guidance says international students won’t be exempt even if an outbreak forces their schools online during the fall term.

The guidance was released the same day Harvard announced it would be keeping its classes online this autumn. Harvard says the directive would prevent many of Harvard’s 5,000 international students from remaining the US.

Harvard president Lawrence Bacow said the order came without notice and that its “cruelty” was surpassed only by its “recklessness”.

“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 other,” Bacow said in a statement on Wednesday.

“This comes at a time when the US has been setting daily records for the number of new infections, with more than 300,000 new cases reported since July 1.”

The guidelines have provoked backlash from universities across the US who say international students have an important place in their communities.