A second person who took part in pro-Palestinian protests at Columbia University has been arrested by U.S. immigration agents, after overstaying a student visa, federal officials said on Friday, the latest turn in the crisis engulfing the Ivy League institution.

The person, identified by the authorities as Leqaa Kordia, is Palestinian and from the West Bank. She was arrested in Newark on Thursday, officials said. Her student visa was terminated in January 2022, and she was arrested by the New York City police last April for her role in a campus demonstration, the Homeland Security Department said in a statement.

The agency also released a video on Friday that it said showed a Columbia student, identified as Ranjani Srinivasan, preparing to enter Canada after her student visa was revoked.

The announcements, by Kristi Noem, the homeland security secretary, reflected an escalation of the Trump administration’s focus on Columbia, where protests over the war in Gaza last year ignited a national debate over free speech and antisemitism, and prompted similar demonstrations at dozens of other campuses.

The actions came during a tumultuous week at the university, which has experienced a series of escalating controversies since the arrest by federal immigration agents last weekend of Mahmoud Khalil, a recent Columbia graduate and prominent figure in pro-Palestinian campus demonstrations.

On Friday, more than 200 students gathered outside Columbia’s main campus gates to protest the university’s handling of Mr. Khalil’s arrest. Demonstrators wore kaffiyehs, waved Palestinian flags and carried banners with slogans like “Free Mahmoud,” “I.C.E. off our campuses” and “Columbia You Can’t Hide.”

The protest unfolded less than 24 hours after homeland security agents entered the campus with federal warrants and searched two dorm rooms. No one was detained and nothing was taken, according to the university’s interim president, Katrina Armstrong.

Social media posts by Ms. Noem on Friday appeared to signal that Columbia continued to be a subject of Trump administration scrutiny.

Ms. Noem posted a video on the social media platform X that appeared to show a woman walking through LaGuardia Airport with a small suitcase. Ms. Noem identified the woman as Ms. Srinivasan and said she had used a U.S. Customs and Border Protection app to notify the government of her intention to self-deport. Ms. Srinivasan’s dorm room was one of those searched, according to her lawyer and roommate.

“It is a privilege to be granted a visa to live and study in the United States of America,” Ms. Noem said in a statement.

Nathan Yaffe, a member of Ms. Srinivasan’s legal team, confirmed in a statement that federal agents had entered her dorm room on Thursday in an effort to detain her or seek information about her whereabouts. A lawyer for Ms. Kordia could not be immediately identified.

The past week has been fraught with crisis on Columbia’s Morningside Heights campus. The Trump administration demanded on Thursday that the university make far-reaching changes to its student discipline and admissions policies before any negotiations regarding the cancellation of $400 million in government grants and contracts could begin.

Federal officials wrote in a letter that the university had a week to formalize its definition of antisemitism, ban the wearing of masks “intended to conceal identity or intimidate” and put the Middle Eastern, South Asian and African Studies Department under “academic receivership.”

The government said the moves were necessary because of what they described as Columbia’s failure to protect Jewish students from harassment. Officials from three government agencies wrote that Columbia “has fundamentally failed to protect American students and faculty from antisemitic violence and harassment.”

Todd Blanche, the deputy attorney general, said during a speech at the Justice Department on Friday that the administration was investigating whether incidents on campus have violated civil rights protections or federal terrorism laws.

“This is long overdue,” Mr. Blanche said.

But civil liberties advocates argued that the government’s demands would not only erode free speech and academic freedom at Columbia but would have a chilling effect on universities across the country. Jameel Jaffer, director of the Knight First Amendment Institute at Columbia, said in a statement that the “subjugation of universities to official power is a hallmark of autocracy.”

Others were particularly concerned by the demand that the university adopt a definition of antisemitism that could penalize those who are critical of Israel.

Tyler Coward, the lead counsel for government affairs at the free speech and legal defense group Foundation for Individual Rights and Expression, called the letter “a blueprint to supercharge censorship at America’s colleges and universities.”

“Colleges across the country are likely reading this letter this morning and thinking they better censor speech — or they’re next,” Mr. Coward said in a statement.

A university spokeswoman said Thursday evening that Columbia was “reviewing the letter” from the government agencies. “We are committed at all times to advancing our mission, supporting our students, and addressing all forms of discrimination and hatred on our campus,” she said.

After the dorm search, Ms. Armstrong said in a note to students and staff members late Thursday that she was “heartbroken” over the development, and that Columbia was making every effort to ensure the safety of its students, faculty and staff.

In a separate action on Thursday, Columbia announced a range of disciplinary actions against students who occupied a campus building last spring, including expulsions and suspensions, among the steps that Trump administration officials had called for in their letter.

The punishments included “multiyear suspensions, temporary degree revocations and expulsions,” the university said in a statement. It was unclear how many students had been punished.

Among those expelled was Grant Miner, a Jewish graduate student who was part of a student coalition that has called for Columbia to divest from companies connected to Israel, according to the student workers’ union at the university, which Mr. Miner leads.

The union has accused the university of targeting its members. A Columbia spokeswoman said Friday evening that it was “unfortunate” that the group was trying to “conflate student discipline with employment matters,” and that the accusation was false.

Mr. Miner, a doctoral student in the English and comparative literature department, said in a statement that “this is an egregious attempt to break the union and squash the movement against genocide in Palestine.”

“We will not be intimidated on either front,” he said.

Anvee Bhutani, Luis Ferré-Sadurní, Hamed Aleaziz, Sharla Steinman and Katherine Rosman contributed reporting.