“We have heard from many of our members, and they all share the same concerns about the nature of the guidance,” said Pedro Ribeiro, a spokesman for the Association of American Universities, which represents 65 research institutions.

ICE said it would not comment on pending litigation.

Kenneth T. Cuccinelli II, the acting deputy secretary of the Department of Homeland Security, defended the agency’s order in an interview Tuesday on CNN, saying that the agency was providing more flexibility for international students than in the past, when in order to qualify for a visa, they could take no more than one of their courses online. 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.”

The Harvard and M.I.T. suit says that the government recognized that the pandemic posed a unique crisis on March 13, when it suspended a rule that students in the country on F-1 student visas had to attend most classes in person. “The government made clear that this arrangement was in effect for the duration of the emergency,” the lawsuit says.

In reversing that earlier guidance on Monday, the universities say, the government has put the ability of international students to continue studying and working in the U.S. in jeopardy, and it has disrupted the careful planning process that many universities have used to restart higher education in the fall, after shutting down campuses in mid-March.

“The effect — and perhaps even the goal — is to create as much chaos for universities and international students as possible,” the universities said in the lawsuit.

International students, many of whom pay full tuition, are a major source of revenue for American universities, and losing them would be a huge blow to the finances of many public and private schools, which are already suffering losses because of the pandemic.