New York City Mayor Eric Adams urged protesters at Columbia University to "walk away" after dozens of demonstrators stormed the campus' Hamilton Hall in what he called a "violent spectacle that serves no purpose."

Adams said the peaceful demonstrations were being co-opted by "professional outside agitators" seeking to "create discord and divisiveness."

"That is why I'm urging every student, every protester to walk away from this situation now. Continue your advocacy through other means," Adams said at a press briefing Tuesday evening. "We will always protect the right to protest, but we must balance that right with the right to keep students in school and our city safe."

"We cannot wait till this situation becomes even more serious. This must end now," he added.

Chief Edward Caban reiterated that protesters who are not Columbia students are working to escalate the situation and said the New York City Police Department is ready to assist the university as needed.

"We have seen the tactics changing in a way that's endangering public safety," he said.

The NYPD showed footage of what Deputy Commissioner for Intel Rebecca Weiner said showed outside actors making barriers inside Hamilton Hall and "escalating" tactics such as scaling buildings and breaking windows. Cameras in the building have also been destroyed, Weiner said.

Individuals who occupied Hamilton Hall could face charges including burglary in the third degree, trespass and criminal mischief, police said.

A Columbia University spokesperson said Tuesday evening that dozens of protesters were in Hamilton Hall.

Some protesters at the University of North Carolina Chapel Hill briefly replaced an American flag with the Palestinian flag on the campus' main quad Tuesday afternoon amid ongoing demonstrations.

The crowd chanted "U.S.A!" and sang "The Star-Spangled Banner" as the American flag was returned to the flagpole, footage shows. The flag was later removed for safekeeping, according to ABC Chapel Hill affiliate WTVD.

The university canceled classes for the rest of the day as of 3 p.m. local time due to the demonstrations on campus.

Education Secretary Miguel Cardona condemned what he deemed the "unacceptable" behavior of protesters on college campuses across the country.

"I think what's happening on our campuses is abhorrent," Cardona told Sen. Shelley Moore Capito, R-W.Va., at the Senate's budget requests hearing for fiscal year 2025 on Tuesday. "It's unacceptable and we're committed as a Department of Education to adhering to Title VI enforcement."

The secretary said the department could reduce federal funds for schools that violate Title VI of the federal Civil Rights Act of 1964, which prohibits discrimination on the basis of race, color or national origin.

Pressed on whether the department was acting to eliminate antisemitism from college campuses amid the growing unrest, particularly at Columbia University, Cardona said the department is reviewing 137 discrimination investigations at Columbia.

He maintained campus safety is of "utmost importance."

"I wouldn't want to send my child to campus if I feel that they're not safe," he said. "That's the most important thing to me -- to make sure that our kids are safe on campus."

-ABC News' Arthur Jones II

Police arrested 79 people at the University of Texas at Austin, Monday and the Travis County Prosecutor's Office has now received 65 cases for criminal trespassing.

"An initial review of the probable cause affidavits does not appear to show deficiencies," Travis County Attorney Delia Garza told reporters Tuesday.

Last week, trespassing charges against protesters were dismissed because they did not show probable cause.

Garza criticized the arrests and charges brought against peaceful protesters and said it is putting a strain on the state's criminal justice system and police response.

"I'm also deeply concerned about how matters will escalate when people believe they are being prevented from exercising their right to participate in nonviolent protest," Garza said.

President Joe Biden addressed the nation on Thursday saying that free speech and the rule of law must both be upheld.

"We are not an authoritarian nation where we silence people or squash dissent, the American people are heard. In fact, peaceful protest is the best tradition of how Americans respond to controversial issues," Biden said, speaking from the White House.

But, he condemned the destruction of property, shutting down campuses and forcing the cancelation of classes and graduation, saying it isn't peaceful protest.

"Dissent is essential to democracy, but dissent must never lead to disorder or to denying the rights of others so students can finish the semester and their college education," Biden said.

Biden last commented on college protests on April 22 -- before there was an escalation of suspension and arrests at campuses across the country -- at the time condemning antisemitic actions and those who don't understand the plight of Palestinians in Gaza, a message he reiterated Thursday.

"There is no place for hate speech or violence of any kind whether it's anti-Semitism, islamophobia or discrimination against Arab Americans or Palestinian Americans. It’s simply wrong. There’s no place for racism in America," Biden said.