Columbia University President Minouche Shafik said that tensions on campus had "rose to new heights" when a group of protesters broke into Hamilton Hall and barricaded themselves. Shafik said it pushed the university "to the brink," according to a letter sent to the Columbia University community Wednesday.

"I know I speak for many members of our community in saying that this turn of events has filled me with deep sadness. I am sorry we reached this point," Shafik said.

The NYPD said it arrested 119 people at Columbia Tuesday night, but it has not yet revealed how many of those arrested are students.

"The University offered to consider new proposals on divestment and shareholder activism, to review access to our dual degree programs and global centers, to reaffirm our commitment to free speech, and to launch educational and health programs in Gaza and the West Bank. Some other universities have achieved agreement on similar proposals. Our efforts to find a solution went into Tuesday evening, but regrettably, we were unable to come to resolution," Shafik said.

Negotiations broke down between the university and members of the encampment after Columbia refused to divest from companies linked to Israel and the war in Gaza.

The University of California, Los Angeles announced that it will cancel all Wednesday classes due to the "distress caused by the violence that took place on Royce Quad" overnight, according to a statement from the university.

The hospital and health system, the Luskin Conference Center and PreK through 12 schools will remain open.

"We have law enforcement presence stationed throughout campus to help promote safety. Student Affairs will have essential staff on campus to support our students who have been impacted by this tragedy," UCLA said in a statement.

At least 12 people have been arrested at the University of Wisconsin-Madison as campus police moved to disperse an encampment of protesters. About 100 to 200 people had arrived for a demonstration Monday and began putting up tents.

The University of Wisconsin said several people resisted arrest, but it is not yet clear how many of the arrested are affiliated with the university.

Several tents have been taken down and dissembled.

"Tents and camping are not allowed on any university property under Chapter 18 of the Wisconsin Administrative Code, which defines the types of activities permitted on campus, information which was shared to all members of the campus community on Friday," the university said in a statement.

The mayor said those who occupied Hamilton Hall were led by people unaffiliated with Columbia University.

Those protesters made a change to more aggressive tactics and represented an "elevated concern," Rebecca Weiner, the NYPD deputy commissioner of intelligence and counterterrorism, said Wednesday.

"The situation had deteriorated to the point where the safety of students, staff and the public was at risk," Police Commissioner Edward Caban said.

There were 282 arrests on a range of mainly minor offenses -- 173 at City College and 119 at Columbia.

"It was a tough decision," Adams said, of the university authorizing the NYPD to move onto campus. "The action had to end and we brought it to a peaceful conclusion."

-ABC News' Aaron Katersky

New York City has received authorization from Columbia University to send the NYPD onto campus, a senior city official told ABC News.

-ABC News' Aaron Katersky