President Biden broke days of silence on Thursday to finally speak out on the wave of protests on American college campuses against Israel’s war in Gaza that have inflamed much of the country, denouncing violence and antisemitism even as he defended the right to peaceful dissent.

In a previously unscheduled televised statement from the White House, Mr. Biden offered a forceful condemnation of students and other protesters who in his view have taken their grievances over the war too far. But he rejected Republican calls to deploy the National Guard to rein in the campuses.

“There’s the right to protest, but not the right to cause chaos,” Mr. Biden said into cameras in his first personal remarks on the campus fray in 10 days. “People have the right to get an education, the right to get a degree, the right to walk across the campus safely without fear of being attacked.” Antisemitism, he added, “has no place” in America.

The president’s comments came as universities across the nation continued to struggle to restore order. Police officers in riot gear arrested about 200 people as they cleared a protest encampment at the University of California, Los Angeles, while other officers removed demonstrators occupying a library at Portland State University in Oregon. Activists erected 30 tents at the University of Wisconsin-Madison a day after the police removed tents and detained 34 people.

The confrontations on Thursday followed a tense 24 hours during which police officers made arrests at Fordham University’s Manhattan campus, the University of Texas at Dallas, Dartmouth College in New Hampshire and Tulane University in New Orleans, among other places. As of Thursday, the campus unrest had led to nearly 2,000 arrests at dozens of academic institutions in the last two weeks, according to a New York Times tally.

Administrators at some colleges, including Brown University in Rhode Island and Northwestern University in Illinois, opted to avoid conflict by striking deals with pro-Palestinian protesters to bring a peaceful end to their encampments — agreements that have drawn harsh criticism from some Jewish leaders.

The protests have erupted in response to Israel’s war in Gaza since the Oct. 7 Hamas-led terrorist attack killed 1,200 people in Israel and resulted in more than 200 taken hostage. More than 34,000 people in Gaza have been killed since then, according to authorities there, including both Hamas combatants and civilians. The protesters have demanded that the Biden administration cut off arms to Israel and that their schools divest from companies linked to Israel, but in many cases the demonstrations have included antisemitic rhetoric and harassment targeting Jewish students.

Some of those sympathetic to the protesters pushed back against administrators for resorting to police action. The Columbia University chapter of the American Association of University Professors on Thursday called for the condemnation of Nemat Shafik, the university’s president, after a police operation that removed students occupying Hamilton Hall and resulted in more than 100 arrests.

“Armed counterterrorism police on campus, student arrests and harsh discipline were not the only path through this crisis,” the group said.

The images of arrests and clashes have come to dominate the political debate in Washington in recent days as Republicans seek to position themselves as defenders of Jewish students and portray Democrats and university leaders as soft on antisemitism.

A day after the House passed a bipartisan measure seeking to codify a broader definition of antisemitism into federal education policy, with 70 Democrats and 21 Republicans voting no, a group of 20 Senate Republicans introduced their own version of the resolution.

“Antisemitism is rearing its ugly head at college campuses across our nation,” said the bill’s sponsor, Senator Tim Scott, Republican of South Carolina and a possible vice-presidential running mate for former President Donald J. Trump. “Jewish students are being targeted with violence and harassment, and the university presidents and administrators, who should be defending them, are caving to the radical mob and allowing chaos to spread.”

Mr. Trump weighed in on social media. “This is a radical left revolution taking place in our country,” he wrote in all capital letters as the confrontation at U.C.L.A. escalated. “Where is Crooked Joe Biden? Where is Governor Newscum? The danger to our country is from the left, not from the right!!!”

Gov. Gavin Newsom of California, a Democrat, issued his own statement on Wednesday. “The right to free speech does not extend to inciting violence, vandalism, or lawlessness on campus,” he said.

That was the formulation that Mr. Biden advanced during his televised comments on Thursday morning before leaving the White House for a daylong trip to North Carolina, where he met with relatives of four law enforcement officers killed in Charlotte on Monday and later gave a speech in Wilmington announcing plans to replace lead pipes.

“Destroying property is not a peaceful protest. It’s against the law,” the president said. “Vandalism, trespassing, breaking windows, shutting down campuses, forcing the cancellation of classes and graduations — none of this is a peaceful protest. Threatening people, intimidating people, instilling fear in people is not peaceful protest. It’s against the law. 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.”

Mr. Biden has been pushing for an agreement between Israel and Hamas that would end the combat, at least temporarily, but a deal has remained elusive. Under a U.S.-sponsored proposal on the table, Israel would enter a cease-fire for six weeks and release hundreds of Palestinians held in its prisons while Hamas would free 33 of the more than 100 hostages it is still holding.

The president and his team hope that such a first stage would lead to a longer cessation of hostilities and the release of more hostages as well as more food, medicine and other aid to ease the humanitarian crisis in Gaza. But American officials said that while Israel has agreed to the plan, Hamas has so far refused.

The president’s four-minute statement came after some Democrats frustrated by his reluctance to speak out pressed him to publicly address the campus uprisings. Until Thursday, Mr. Biden had offered only a couple of sentences in response to reporter questions on April 22 that even Democrats considered too equivocal and otherwise left it to his spokespeople to express his views. Republicans have castigated him for not weighing in himself.

Mr. Biden implied that his critics were simply being opportunistic. “In moments like this, there are always those who rush in to score political points,” he said. “But this isn’t a moment for politics. It’s a moment for clarity. So let me be clear: Peaceful protest in America. Violent protest is not protected. Peaceful protest is.”

In calming some in his party, though, Mr. Biden took heat from others on the political left. In their view, he employed none of the nuance that he expressed in 2020 when otherwise peaceful protests after the police killing of George Floyd got out of control and Mr. Biden acknowledged root causes of the anger even while condemning violence.

“He could’ve made some effort to do the same today,” said Matt Duss, a former foreign policy adviser to Senator Bernie Sanders, the democratic socialist from Vermont. “Instead, he chose to amplify a right-wing caricature. Unfortunately, it’s consistent with an overall policy approach that shows little regard for Palestinian perspectives or Palestinian lives.”

In his statement, Mr. Biden emphasized that he would always defend free speech, even for those protesting his own support for Israel’s war. But he made clear that he thought too many of the demonstrations had gone beyond the bounds of simple speech.

“Let’s be clear about this as well,” he added. “There should be no place on any campus, no place in America, for antisemitism or threats of violence against Jewish students. There is no place for hate speech or violence of any kind, whether it’s antisemitism, Islamophobia, or discrimination against Arab Americans or Palestinian Americans.”

In response to questions by reporters, Mr. Biden said he would not change his Middle East policy as a result of the protests. Asked as he left the room if the National Guard should intervene, he said simply, “No.”

Reporting was contributed by Jonathan Wolfe from Los Angeles; Ernesto Londoño from St. Paul, Minn.; Bob Chiarito from Madison, Wis.; and Mike Baker from Seattle.