Kyle Chapman expected he might find a fight. And he did — with a teenage girl.

The girl was waving an anti-fascist placard last week at a protest against Shariah law in Midtown Manhattan when a scuffle broke out and she knocked an older woman to the ground.

“Assaulting our people?” Mr. Chapman shouted as he reached across the barricades and ripped her sign apart. “Your days are numbered, Commie!” he called after her as the police escorted her away. “The American people are rising up against you!”

As the founder of a group of right-wing vigilantes called the Fraternal Order of Alt-Knights, Mr. Chapman, a 6-foot-2, 240-pound commercial diver, is part of a growing movement that experts on political extremism say has injected a new element of violence into street demonstrations across the country.

Part fight club, part Western-pride fraternity, the Alt-Knights and similar groups recruit battalions of mainly young white men for one-off confrontations with their ideological enemies — the black-clad left-wing militants who disrupted President Trump’s inauguration and have protested against the appearances of conservative speakers on college campuses.

Along with like-minded groups like the Proud Boys, a clan of young conservative nationalists, and the Oath Keepers, an organization of current and former law-enforcement officers and military veterans, they mobilized on social media to fight in New Orleans over the removal of Confederate monuments; on the streets of Berkeley, Calif., where clashes between the left and right have increasingly become a threat for law enforcement; and at a raucous May Day rally in Los Angeles.

Both sides have issued a call to arms this weekend for an event being billed as a “Trump Free Speech Rally” in Portland, Ore., which is already on edge after a man was charged in the murder of two people who tried to intercede last week as he hurled anti-Islamic insults at two women on a train. “This is a war,” declared the Proud Boys’ founder, Gavin McInnes, in a column this week.

Law enforcement has taken notice. At the protest last week at the City University of New York, which had been heavily promoted on social media, throngs of police officers lined the sidewalk before it began. In Portland, the police said they were mobilizing a robust presence because of what they have seen online. “It’s almost like a street fight, like a rumble, the way it’s being advertised,” said Sgt. Pete Simpson, a spokesman.

Many in the movement, like Mr. Chapman and Mr. McInnes, say they are supporters of Mr. Trump’s agenda to tighten immigration and fight political correctness. While Mr. Trump has recently taken steps to denounce hate speech and violence, the proliferation of militant groups on both the left and the right is part of the new reality of political expression. Advocates who track extremism say the president, who egged on violent supporters during his campaign, has played a role in emboldening the groups.

To Mr. Chapman, 41, who on social media goes by the nom de guerre Based Stickman — “based” is slang for not caring what others think, and “stickman” refers to the closet dowel he wielded this spring at his first political skirmish — the Alt-Knights are a frustrated brotherhood of right-leaning soldiers conscripted to do battle with the left and devoted, as he put it in a Facebook post in April, to “defense and confrontation.”

“There’s been a lot of organized violence on the part of the left against the right, so we have to organize,” Mr. Chapman said. “The purpose is to have a peaceful event. But if people are attacked, you have to be ready and willing to defend yourself and your right-wing brothers and sisters.”

This form of aggression is something researchers say they have not seen on such a scale before on the far right, where the chosen method of provocation for groups like neo-Nazis and the Ku Klux Klan is to demand the use of public space for rallies where they can spew racist and offensive language that is nonetheless protected as free speech.

“These are new people to us,” said Heidi Beirich, the Intelligence Project director for the Southern Poverty Law Center, which tracks extremist movements.

Typically, the far-right groups they study will demonstrate but avoid confrontation, acting in a “defensive crouch,” she added.

“But saying, ‘We’re going to show up and we’re intending to get in fights,’ that’s a new thing,” Ms. Beirich said.

Some groups like the Proud Boys have initiation rituals that include violent hazing and require an oath of fealty to Western culture. Their followers thrive on hyper-masculinity and celebrate when one of their brethren hits a leftist agitator. They mock Islam and purport to be soldiers against a “war on Whites,” while being mindful not to embrace overt white supremacy. Roger J. Stone Jr., a longtime associate of Mr. Trump’s, has taken the Proud Boy oath.

The Alt-Knights were initially conceived as a paramilitary wing of the Proud Boys, designed to provide protection for audiences listening to conservative speakers like Ann Coulter and Milo Yiannopoulos, whose public events have been canceled because of threats of violence.

The groups openly post on Facebook and Twitter to spout Islamophobic and anti-immigrant speech, recruit new members and mobilize followers to go to demonstrations where violence might erupt, taking advantage of the porous standards that social media companies set for offensive and violent speech.

The internet commerce businesses PayPal and GoFundMe recently blocked Mr. Chapman from accepting money from supporters. He also said he has been barred twice from Facebook, though only temporarily. But his Facebook account, which has about 33,000 followers, remains a source of Islamophobic posts and calls for others to join him at events where clashes are likely.

The founder of the Proud Boys, Mr. McInnes, 46, a Canadian with a hipster-lumberjack aesthetic, is no stranger to controversy. He helped found Vice Media and edited its edgy magazine before leaving in 2007 over differences with his partners. In one episode that drew his colleagues’ ire, he told The New York Times in 2003, “I love being white.”

Mr. McInnes has seemed to find sophomoric pleasure in offending liberals, feminists, “beta male culture” and transgender people. His work is often inflected with a tone of crass, satirical bigotry that leaves him just enough room to declare it all a joke. While Mr. McInnes insists that the Proud Boys are “are a normal fraternal organization like the Shriners,” the sentiments that unify its members are often tinged with disrespect for nonwhite culture.

Of white men, he once wrote: “We brought roads and infrastructure to India and they are still using them as toilets. Our criminals built nice roads in Australia but aboriginals keep using them as a bed.”

In Berkeley in April, Mr. McInnes and a gang of Proud Boys gathered after Ms. Coulter, the conservative commentator, pulled out of an appearance over security concerns.

Things quickly turned boozy and bizarre. After a few remarks, Mr. McInnes initiated a new group of Proud Boys, some wearing “Make America Great Again” hats. The first ritual, as captured on video and explained by a member, was to “announce yourself as a white, proud Western chauvinist, make sure everyone knows it, and don’t be ashamed.” In a second ritual, the recruits were punched repeatedly until they recited the names of five breakfast cereals.

The use of ironic, juvenile antics is something commonly seen on the fringes of the right because it allows a veneer of deniability, experts said. “It gives them an out, a gray area where they can make this safe space to say what they want,” said Carla Hill, a researcher for the Anti-Defamation League’s Center on Extremism.

Mr. Chapman described himself as a student of history, a lover of combat and a right-wing warrior bent on ridding the United States of “neo-Marxists” and “Communist domestic terrorist organizations.” Though he now lives in the Bay Area, he was raised in San Diego and Houston, where, court records say, he had a taste for huffing Scotchgard fabric spray. As a youth, he said, he often tussled with Latino gangs and claimed to have been shot and stabbed twice before he graduated from high school.

“It was a very violent environment,” Mr. Chapman said. “You’d go down to the boardwalk, you’d drink and get in a fight, and that would be a great Friday or Saturday night.”

Mr. Chapman voted last year for Mr. Trump and now refers to himself as an “American nationalist.” During the campaign, he watched from the sidelines as scuffles erupted at Mr. Trump’s events, but could not take part because at that point, he was on parole from a federal weapons charge — one of his three felony arrests.

Then, in February, he saw the footage on television of Kiara Robles, a young Trump supporter, getting pepper-sprayed by an anti-fascist activist. “I said to myself, ‘You know what?’” he recalled. “‘That’s it. I’m done.’”

By then he was off parole, and on March 4, he attended a Trump rally in a public park in Berkeley, carrying his closet dowel and clad in ersatz armor: a baseball helmet, a gas mask, ski goggles, shin pads, a wooden shield. When Mr. Chapman clubbed a demonstrator over the head, he earned his nickname and became a hero to the “I’m mad as hell” right after his arrest.

That was when he became acquainted with Mr. McInnes, who reached out to tell him that a Proud Boy in Berkeley had created a fund to pay his bail. “He’s a great guy,” Mr. McInnes said. “I wanted to make him president of the Proud Boys, but it makes more sense that he runs the Alt-Knights.”

Aside from his encounter with the teenage girl, Mr. Chapman remained fight-free last week at the Shariah law protest. He mostly roamed the crowd, snapping selfies with his fans, followed by a flock of acolytes, some of whom, in homage to him, were dressed in pads and helmets, and carried heavy sticks.

Later that day, Mr. McInnes gave a party in an unmarked bar on Lexington Avenue. There were Alt-Knights, Proud Boys, bikers in leather vests and young guys with the American flag around their necks. Though the crowd was mostly white men, there were women, a few black people and Latinos. After three or four hours, a rowdy mood set in.

“I have a question!” Mr. Chapman shouted at one point, commanding the attention of the room. “What do we stand for?”

“Freedom!” people yelled.

“And what do we bleed for?” Mr. Chapman shouted.

“Freedom!” they yelled again.

He suddenly grabbed the man beside him.

“Are you ready to bleed?” Mr. Chapman shouted at the man.

“I’m ready to bleed!” he yelled.