The statement comes as there was a clash between protesters during the day Friday. The tense scene on campus had calmed down as of Friday evening.
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President Paul Alivisatos said protesters have expressed their views for the last four days.
"Out of principle we provide the greatest leeway possible for free expression, even expression of viewpoints that some find deeply offensive, even in rare cases at the expense of some policy violations-for a time," he said.
Alivisatos and the provost met with protesters Thursday, and said they "shared genuine and powerful statements about what has brought them to the encampment."
He said he regrets they have not yet found common ground.
"The nature of their demands are such that we could not accede. There remain, however, numerous ways consistent with our principles and policies for the protesters to advance their views. We are prepared to support meaningful engagement on the issues that the protesters have called attention to," Alivisatos said.
He added that previously the university said it would only intervene if the protests blocked the learning or expression of others or substantially disrupted the functioning or safety of the school.
"Without an agreement to end the encampment, we have reached that point," he said.
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Alivisatos added that the encampment has created systematic disruption on campus, including disrupted learning, destruction of an approved installation of Israeli flags, shouting down speakers, vandalism and graffiti on historic buildings and co-opting the university flagpole to fly the Palestinian flag.
"I hope that he takes action soon so that more of these escalations don't happen," said Joshua Weisskopf, University of Chicago senior student and president of Maroons for Israel.
He also said the encampment is stretching police resources.
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A spokesperson for UChicago United for Palestine also said the group could not reach an agreement with the university. The organization's demands include disclosing the school's investments.
Just after 1 p.m., UChicago said in a post on X, formerly Twitter, "please avoid the Main Quad area. Reports of physical altercations."
There were some tense moments Friday, as students holding American flags began marching into the encampment.
Chopper 7 over dueling protests at UChicago
The altercation turned physical at one point, eventually forcing campus police to step in.
Five days into the encampment, some counter-protesters decided to take action.
Dozens of students were holding American flags, chanting USA and singing the national anthem.
Both sides stood firm, shouting dueling chants at one another. Then, some protesters began shoving. A brief scuffle broke out, with emotions running high.
"We are Americans. We stand for the freedom of speech, but what we don't stand for is vandalism and occupying things, blocking students. We are here to study. We're here to learn, and they are impeding that. And we're not going to stand for that," UChicago student Arthur Long said.
Jewish students with Maroons for Israel were having a peaceful picnic at the time, steps away.
"It's pretty upsetting. Nobody wants to see escalation. Nobody wants to see students and peers pitted against each other," Talia Elkin said.
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Pro-Palestinian protester Hassan said he was not there to escalate the situation.
"We are here to achieve our demands," Hassan said. "If they (university officials) want to intervene, it's a sign of how deep their complicity is. But we are standing here, steadfast in solidarity with Gaza and in strength with our demands of divestment."
The university has not said when or how it plans to intervene.
"We understand that the university is willing to give us criminal records before degrees, and I don't think that a raid is beneath them," said Youssef Hasweh, University of Chicago senior student and pro-Palestinian protester.
Arrests at campus protests across the country had President Joe Biden weighing in Thursday.
He cast the protests as a balance between two fundamental American ideals: the right to freedom of speech and assembly and the rule of law.
"So, let me be clear, peaceful protest in America: Violent protest is not protected. Peaceful protest is," Biden said. "Threatening people, intimidating people, instilling fear in people is not peaceful protest; it's against the law."
Jewish students at University of Chicago previously said the demonstration there continues to make them feel uncomfortable, especially if there are non-students involved.
"It's more nuanced than people sort of yelling slurs at me. I think we can be made to feel unsafe even if people aren't yelling slurs," said Matthew Wieseltier, a University of Chicago Jewish student.
There have been thousands of arrests at college demonstrations nationwide. About half of them at campuses in New York were of people not affiliated with any university.