BERKELEY, Calif. — Fires burned in the cradle of free speech. Furious at a lecture organized on campus, demonstrators wearing ninja-like outfits smashed windows, threw rocks at the police and stormed a building. The speech? The university called it off.

Protest has been synonymous with the University of California, Berkeley, from the earliest days of the free speech movement, when students fought to expand political expression on campus beginning in 1964. Those protests would set off student activism movements that roiled campuses across the country throughout the 1960s. Since then, countless demonstrators have flocked to Sproul Plaza each day to have their voices heard on issues from civil rights and apartheid to Israel, tuition costs and more.

But now the university is under siege for canceling a speech by the incendiary right-wing writer Milo Yiannopoulos and words like intolerance, long used by the left, are being used by critics to condemn the protests on Wednesday night that ultimately prevented Mr. Yiannopoulos from speaking.

Naweed Tahmas, a junior who is a member of the Berkeley College Republicans, the group that invited Mr. Yiannopoulos to campus, said the cancellation had made him more determined to fight for freedom of speech on campus.

“I’m tired of getting silenced, as many conservative students are,” he said. “If we support freedom of speech, we should support all speech including what they consider hate speech.”

When the event was canceled, the Republican student group reacted by writing on their Facebook page, “the Free Speech Movement is dead.”

More than 100 faculty members signed a letter opposing the visit by Mr. Yiannopoulos in recent weeks. “We support robust debate, but we cannot abide by harassment, slander, defamation, and hate speech,” they wrote.

On Thursday, heated arguments broke out at Sproul Plaza between students who said Mr. Yiannopoulos — a provocateur editor at Breitbart News who is known for his attacks on political correctness and offensive, racially-charged writing — was too inflammatory to be invited to campus and those who argued that he should have been allowed to speak.

The university made it clear they believed the people who resorted to violence on Wednesday night — a group, clad in black clothing and carrying sticks — had come from outside the campus. The university estimated on Thursday that the rioting had caused around $100,000 in damage.

Whatever the origins of the violent mob, the university was and remains divided over the meaning of free speech at a time of national political tumult.

“I think we need to have a serious conversation about protests. This is going to be a big part of our lives for the next four years,” said Kirsten Pickering, a graduate student at the university. She and others described the violence as a “potential teachable moment.”

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“We need to sit down and talk about what is acceptable,” she added.

Troy Worden, a third-year student and a member of the College Republicans, said he would “absolutely” invite Mr. Yiannopoulos to speak on campus again, and Mr. Tahmas added that the Republican student group is a racially diverse group that does not consider Mr. Yiannopoulos to be a white nationalist.

Criticism of the decision to cancel the speech came from outside the university as well. On Twitter early on Thursday, President Trump went as far as to threaten withholding federal funds from the university for failing to stop “violence on people with a different point of view.”

Since embarking in September on his speaking tour of American campuses, he has been trailed by protests. But the events have also attracted pockets of self-described anarchists clad in face masks and spoiling for a fight. Some university organizers withdrew invitations to Mr. Yiannopoulos over security concerns. At the University of California, Davis, on Jan. 13, his speech was canceled as it was set to begin after a tense standoff between protesters and police officers. A week later, on Inauguration Day, a man was shot during protests outside Mr. Yiannopoulos’s speech at the University of Washington in Seattle.

He was to cap his tour this week at Berkeley. In the weeks leading up to the event, campus administrators faced tremendous pressure from student groups and faculty members to cancel it.

In a video of himself posted on Facebook after the cancellation on Wednesday night, Mr. Yiannopoulos criticized the “hard left, which has become so utterly antithetical to free speech in the last few years.”

“They simply will not allow any speaker on campus, even somebody as silly and harmless and gay as me to have their voice heard,” he added.

One group that has been outspoken in favor of allowing Mr. Yiannopoulos to speak is the veterans of the university’s free speech movement.

“I’m really a little fatigued with all of this, ‘Oh my goodness, cover my ears, someone will say something that will upset me, I can’t tolerate that,’ ” said Jack Radey, who was a 17-year-old activist during the original free speech movement at Berkeley.

“There are racists, sexists, piggery of various kinds who will say really terrible things. And that is part of the world,” Mr. Radey said by telephone from Oregon, where he is retired. “Learn how to fight back. Don’t say, ‘Oh, no. We can’t allow someone to speak because someone might be offended.’ ”

In a letter to The Daily Californian, Berkeley’s student newspaper, Mr. Radey and other members of the Free Speech Movement Archive board of directors, a grouping of some of the movement’s activists, said Mr. Yiannopoulos was “a bigot who comes to campus spouting vitriol so as to attract attention to himself.”

But they said free speech was paramount.

“Berkeley’s free speech tradition, won through struggle — suspension, arrest, fines, jail time — by Free Speech Movement activists is far more important than Yiannopoulos, and it is that tradition’s endurance that concerns us,” they wrote.