Harvard University and the Massachusetts Institute of Technology sued the Trump administration Wednesday over an order that would require international students to take classes in person this fall, despite rising coronavirus caseloads that are complicating efforts by colleges and universities to offer in-person learning.

The lawsuit represented a swift response to an unexpected order issued this week by the federal government, as universities rush to protect the status of thousands of international students. It also marks a new battle line in the war between President Trump and education leaders over how to safely reopen schools in the midst of his reelection bid.

“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’s president, Lawrence S. Bacow, told the Harvard community Wednesday.

On Wednesday, Northeastern University in Massachusetts joined the suit, with Joseph E. Aoun, the school’s president, saying the new guidance “creates chaos for international students and has the effect of weakening American higher education — one of our nation’s signature strengths.”

On Monday, the federal Student and Exchange Visitor Program announced that visas would not be issued to students enrolled in schools that are fully online this fall. Under the rule, those students would be barred from entering the country. And to keep their visas, students already in the United States would need to leave the country or transfer to a school with in-person instruction.

The rule has not been published yet, but the guidance issued Monday stunned university officials and panicked students. Though international students were previously required to take classes in person, the government had offered schools and students flexibility this spring, after the pandemic shut down most campuses. And it had said that the new guidance would remain in effect for the duration of the emergency.

So as university officials worked to finalize fall plans, many assumed that their international students would be allowed in the country even if they weren’t in the classroom. With cases rising across the country, most colleges are at least prepared to switch to fully virtual instruction if needed. Others, including Harvard and the sprawling California State University System, have already announced plans to offer little to no in-person instruction.

Harvard has about 5,000 international students, and MIT 4,000. In their lawsuit, the universities argue that U.S. Immigration and Customs Enforcement’s decision was designed to force universities to conduct in-person classes, part of an apparent political strategy from the Trump administration to pressure schools, from kindergarten to graduate school, to fully reopen this fall, even as virus cases soar.

The lawsuit, filed in the U.S. District Court in Massachusetts, seeks a temporary restraining order that would quickly stop the government from enforcing the policy. The schools argue that the rule violates the Administrative Procedure Act, which governs rulemaking by federal agencies.

The Department of Homeland Security did not immediately respond to requests for comment. Carissa Cutrell, a spokeswoman for ICE, said the agency “is unable to provide further comment due to pending litigation.”

The lawsuit cites remarks from acting deputy secretary of homeland security Ken Cuccinelli on Tuesday, in which he said the directive “will … encourage schools to reopen.”

The decision also reflects the administration’s continued efforts to limit and reduce the presence of international students in the country, the lawsuit argues.

The Trump administration contends the new policy will provide more flexibility for colleges and universities. Cuccinelli indicated Tuesday that international students could remain in the United States as long as they receive at least some face-to-face instruction.

“Anything short of 100 percent online classes,” he told  an interview. Cuccinelli denied that the administration was seeking to “force” universities to offer in-person teaching. But he acknowledged that the administration wants to spur movement in that direction. “This is now setting the rules for one semester, which we’ll finalize later this month that will, again, encourage schools to reopen,” he told.

The ICE ruling frightened international students, who worried they risked deportation if their schools were not providing classes in person.

“That’s horrifying — I couldn’t sleep,” said Mita Rawal, who’s studying pharmacology at the University of Georgia. “It’s not just me, it’s my son, he goes to school here. If I had to pack up my bags and go to Nepal,” she said, and then broke off.

She had already been through a tumultuous spring and summer, with a sudden need for a computer for her own studies and a secondhand laptop for her 5-year-old son’s schooling, paid for with the help of an emergency grant from a nonprofit. Her dissertation was put on hold, and she was unable to travel home for the summer.

And then news broke from ICE. “I had not anticipated in my wildest dreams that I would be in this situation,” she said.

Outraged faculty are mobilizing to defend international students. Some are brainstorming ways to work around the administration’s policy, creating makeshift classes for international students.

Dana R. Fisher, a sociology professor at the University of Maryland at College Park, said she woke up Wednesday to 25 emails from terrified students. She had fielded even more frantic emails the day before. On Twitter, she offered an independent-study course to any student who needs to take an in-person class this semester. Dozens are interested, she said.