Harvard University sued the Trump administration for a second time on Friday, less than 24 hours after the Department of Homeland Security said it would block international students from attending the nation’s oldest university and one of its most prestigious.

The lawsuit, and a letter issued by Dr. Alan M. Garber, Harvard’s president, signified a dramatic escalation of the battle between the administration and Harvard. And the university’s forceful and almost immediate response served as evidence that stopping the flow of international students to Harvard, which draws some of the world’s top scholars, would destabilize Harvard’s very existence.

“We condemn this unlawful and unwarranted action,” Dr. Garber said in a letter to the Harvard community. “It imperils the futures of thousands of students and scholars across Harvard and serves as a warning to countless others at colleges and universities throughout the country who have come to America to pursue their education and fulfill their dreams.”

The lawsuit followed an announcement on Thursday that Harvard’s Student and Exchange Visitor Program certification had been revoked, halting the university’s ability to enroll international students. The university indicated that it would also be filing a request for a temporary restraining order asking a judge to immediately block implementation of the administration action.

In the lawsuit, the university accused the Trump administration of retaliating against Harvard for exercising its First Amendment rights.

The administration said Harvard had not complied with a list of demands sent on April 16 that contained records of protest activity dating back five years, including videotapes of misconduct and records of disciplinary actions involving international students.

Harvard’s lawsuit also said that the university had been working to comply with the April 16 request, along with a letter attacking the university for failure to condemn antisemitism.

The Trump administration has explained its attacks on Harvard and other top private universities as an effort to combat antisemitism and confront liberal biases on campus. During his campaign, Mr. Trump invoked the term “Marxist maniacs” to refer to the Ivy League.

After he was inaugurated, Mr. Trump’s administration has sought to use nearly every lever the federal government has at its disposal to force schools, Harvard especially, to bend to its will. There are now at least eight investigations into Harvard spanning at least six federal agencies.

Separately, the Trump administration had sought to use the federal government’s international student system as a way to remove foreign nationals from the country. Immigration officials targeted a handful of pro-Palestinian student activists, but also ended the legal status of hundreds of students, creating a general anxiety among international students at colleges and universities nationwide. (Most of those students have had their status restored, but a few high-profile cases are being argued in the courts.)

This is a developing story. Please check back for updates.