Harvard and M.I.T. said on Wednesday that they had filed a lawsuit against the Trump administration over a directive that would strip foreign students of their visas if their coursework was entirely online.

The White House measure, announced on Monday, was seen as an effort to pressure universities into reopening their gates and abandoning the cautious approaches that many have announced they would adopt to reduce transmission of the coronavirus.

“The order came down without notice — its cruelty surpassed only by its recklessness,” Harvard’s president, Lawrence S. Bacow, said in a message to the university community.

“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.”

The directive’s effect may be to dramatically reduce the number of international students enrolling in the fall. Together with delays in processing visas as a result of the pandemic, immigrant advocates say the new rules, which must still be finalized this month, might discourage many overseas students from attending American universities, where they often pay full tuition.

But the concern that their campuses could become coronavirus clusters has prompted many universities to adopt measures to reduce exposure, from requiring masks in classrooms to limiting social activities to reducing the number of students invited back to campus. Many have announced a hybrid approach that would provide some in-person classes but offer a significant amount of coursework virtually.

Such changes could put foreign students’ visas, known as F-1 visas, at risk under the new rules. International students whose universities are not planning in-person classes — which is currently the case at schools including Harvard and the University of Southern California — would be required to return to their home countries if they are already in the United States. Those overseas would not be granted permission to enter the country to take online coursework here.

Kenneth T. Cuccinelli II, the acting deputy secretary of the Department of Homeland Security, said in an interview on CNN that the administration was providing more flexibility for international students than in the past, when they could only take one online course to qualify for visas. Now they can take more, as long as at least some of their instruction is in person.

“If they’re not going to be a student or they’re going to be 100 percent online, then they don’t have a basis to be here,” Mr. Cuccinelli said, adding, “They should go home, and then they can return when the school opens.”