The steps in front of Low Memorial Library at Columbia University have been the site of major campus protests since the 1960s. But when pro-Palestinian demonstrators tried to organize a rally there last Thursday, the area was barricaded off.

When the students instead joined a rally on the streets outside of campus the next day, they were greeted by rows of police officers. The scene was heated; 15 people were taken into custody.

Since the beginning of the Israel-Hamas war, Columbia has been under intense pressure to rein in pro-Palestinian protests that accuse Israel of genocide and call for a cease-fire. The protests have not been violent, but some donors, trustees and students say they reflect and foment antisemitism. In response, Columbia and Barnard, the university’s sister school, have sought to enforce rules requiring extensive advance notice and barring anything that might disrupt campus activities.

The measures have reduced protests. But, some students say, they have also violated free speech rights, and challenged long traditions of political protest on campuses that were historically the scenes of raucous rallies about everything from the Vietnam War to South African apartheid.

And by limiting campus demonstrations about the war, the students say, the school is pushing them onto the city’s streets, where protests can sometimes turn dangerous.

Often organized by established activist groups, the demonstrations have shut down traffic and shut off access to city landmarks, and the police have responded in force and made numerous arrests.

“One of us might get really hurt badly. Because we are not backing off,” said Mohsen Mahdawi, a co-founder of Dar, the school’s Palestinian student union. “We see a serious problem; we see a humanitarian call to stand up for ending the killing of Palestinians.”

A Columbia spokesman said that it was the administration’s job to support everyone on campus and that the university had “a responsibility to support all members of our community as they study, teach and research on our shared campus.”

The reason Columbia blocked access to the Low Library steps on Thursday was because it did not want an event inside to be disrupted, officials said. There was an evening gala celebrating the 75th anniversary of Columbia’s East Asian Institute, with a keynote speech by John Kerry, the former secretary of state.

Jennifer Fondiller, a spokeswoman for Barnard, expressed a similar sentiment. “We support our students’ right to free expression, but we also have an obligation to maintain a safe and conducive learning environment for our entire community on our four-acre campus,” she said.

After the war in Gaza broke out in October, tensions on campuses around the country ratcheted up almost immediately. At Columbia, two pro-Palestinian student groups were suspended in the fall semester for holding unauthorized protests, and students, professors and members of Congress accused the university of allowing pro-Palestinian demonstrations that they said promote antisemitism.

Columbia is among dozens of American colleges now being investigated by the federal Department of Education after complaints of antisemitism or anti-Muslim sentiment on campus. While there has been little violence by demonstrators, some supporters of Israel have argued that some of the chants during pro-Palestinian marches are offensive and antisemitic. In the fall, Columbia cited unspecified “threatening rhetoric and intimidation” when it banned the pro-Palestinian student organizations.

But instead of barring specific words or phrases that could be seen as discriminatory, Columbia and other colleges have been taking a more bureaucratic approach to rein in protests and rallies. At Barnard, for example, most protests now have to give 28 days’ notice, or they will be considered unauthorized and students participating could risk discipline.

Rules at Columbia require 10 business days’ notice before a protest. Protests also typically cannot be held in buildings, where they could disrupt academic activity and campus life.

Barnard administrators have summoned about 20 students to disciplinary hearings and accused them of participating in an unauthorized pro-Palestinian student rally in December, according to The Columbia Spectator. While the students have received only warnings so far, the message has been clear that if they are caught again, more serious discipline will follow, several students and professors who attended the hearings said.

But the schools are also facing an opposing demand from many students and faculty to give a wider berth to freedom of speech and academic freedom, even if some people consider the views being expressed hateful and intimidating.

“I think that the student right to protest is the fundamental core value of what a liberal arts education is about,” said Premilla Nadasen, a historian at Barnard. “It’s part of the student’s democratic engagement with the world around them. And I find that vanishing at both Barnard and Columbia.”

Eliana Goldin, a junior at Columbia, is the co-chairwoman of Aryeh, a pro-Israel student organization. She said that while she thought the campus rule requiring 10 days’ notice for a protest was excessive, she didn’t think Columbia was yet holding anyone accountable for it, as she still encounters a pro-Palestinian demonstration on campus at least once a week.

She said the rules affected pro-Israel students less, as they seem less eager to protest. “I think many Jews are just really trying to get through the day,” she said.

The show of force that met protesters last Friday, when hundreds of students and others gathered just outside Columbia’s gates, shocked some of them.

“The way that they showed up with dozens of police cars, with wrist ties and all this stuff, it looked like they were preparing for war instead of a peaceful protest,” said Layla Saliba, a 24-year-old Palestinian American graduate student at the Columbia School of Social Work.

The afternoon had started with a small protest outside the inauguration of Laura Rosenbury, the new president of Barnard, who has faced criticism for her handling of student protest issues on campus. Some students also disrupted her remarks.

The action then moved to the corner of 116th Street and Broadway, where more community and student groups had began to gather. The event was mainly organized by Within Our Lifetime, a pro-Palestinian activist organization that has been running major protests throughout New York City since the start of the war.

Protesters said that the police had demanded that they stay in a small barricaded area and threatened them with arrest if they used a bullhorn to shout slogans. After several angry scuffles with the police, protesters left the enclosure and began to march around the campus.

The police warned the protesters that if they disrupted traffic they could be arrested. Columbia students who tried to re-enter campus found the main gates locked, they said. The police arrested some marchers, leading to angry reactions and brawls. In all, 12 people received summonses and three were arrested, including one Columbia student, the police said. The Police Department did not respond to a request for comment about officers’ actions during the protest.

In chants on Friday, protesters compared the Police Department to the Ku Klux Klan and the Israel Defense Forces. Another chant claimed, “There is only one solution: intifada, revolution.”

The march was held in part to demand more action in response to an alleged attack in which someone used a foul-smelling substance against pro-Palestinian student protesters on campus in January. The police said that they were still investigating the episode and that no arrests had been made. Columbia said it had barred the students suspected in the attack from campus while the investigation proceeds.