Far-right groups celebrated on social media after President Donald Trump responded to a debate question about white supremacists by saying that the extremist Proud Boys, a male-only group known for its penchant for street violence, should "stand back and stand by."

Starting Tuesday night and continuing Wednesday, Trump's comments were enshrined in memes, including one depicting Trump in one of the Proud Boys' signature polo shirts. Another meme showed Trump's quote next to an image of bearded men carrying American flags and appearing to prepare for a fight. A third incorporated "STAND BACK AND STAND BY" into the group's logo.

Such images spread quickly on the conservative social media site Parler and channels on the encrypted chat app Telegram, according to researchers.

One prominent Proud Boys supporter on Parler said Trump appeared to give permission for attacks on protesters, adding that "this makes me so happy." Others saw a retail opportunity, pushing $30 T-shirts and $40 hoodies bearing the group's logo and the words, "PROUD BOYS STANDING BY."

On the fringe social media site 4chan, an anonymous supporter wrote, "STAND BACK AND STAND BY … SOMEONE HAS TO STOP THESE FAR LEFT RIOTERS," according to SITE Intelligence Group, which tracks far-right groups.

Mainstream platforms such as Facebook, Twitter and YouTube have cracked down on the Proud Boys for violating policies against hate speech. Twitter and Facebook acted in 2018. YouTube has quickened the pace of enforcement against violent right-wing extremist groups since updating its hate-speech policy last year.

The Proud Boys, like other extremist groups, have found new homes online, especially on Telegram, and new visibility, thanks to Tuesday night's debate. One researcher said memberships to three Proud Boys channels on Telegram grew nearly 10% after the debate.

"He legitimized them in a way that nobody in the community expected. It's unbelievable. The celebration is incredible," said Rita Katz, executive director of SITE. "In my 20 years of tracking terrorism and extremism, I never thought I'd see anything like this from a U.S. president."

SITE found that Telegram channels devoted to neo-Nazis and white supremacists portrayed Trump's comments as signals of support. The Proud Boys dispute characterization as white supremacists, but their actions are often touted by white supremacists and others on far-right political fringes.

Twitter also experienced a huge spike in references to Proud Boys: more than a million since Trump's statement and about 75,000 an hour on Wednesday morning, according to Clemson social media researcher Darren Linvill. The group more commonly averages a few thousand references on Twitter per day.

Trump's comments came in response to a question from the moderator, Fox News anchor Chris Wallace, about whether he would be willing to publicly denounce white supremacists. The president initially suggested he would, but when Democratic nominee Joe Biden asked specifically about the Proud Boys, Trump responded, "Proud Boys, stand back and stand by. But I'll tell you what, somebody's got to do something about antifa and the left."

The Trump campaign tweeted afterward: "President Trump has repeatedly condemned white supremacists. What a ridiculous question from Chris Wallace." And on Wednesday, Trump told reporters that he did not know who the Proud Boys were.

"I mean, you'll have to give me a definition, because I really don't know who they are. I can only say they have to stand down. Let law enforcement do their work," Trump said.

Trump and his Cabinet have sought in recent months to portray political violence as predominantly a problem of far-left groups, including the loosely organized antifa. But independent researchers on political extremism and terrorism have consistently concluded that white supremacists and the far right generally have been more dangerous in recent decades.

The prospect of Election Day violence has increasingly concerned those who monitor such groups. The Michigan chapter of the Proud Boys, one of those that made memes featuring Trump's quote Tuesday night, had recently urged people on Telegram to become "poll challengers" on Election Day.

Trump sounded similar themes in the debate, urging his supporters to monitor polling places for supposed acts of fraud. Later, the Trump campaign ran advertising encouraging people to become poll workers.

"You're essentially telling a paramilitary force to 'stand by,' " said Heidi Beirich, an expert on far-right politics who co-founded the Global Project Against Hate and Extremism. "I think at this point, the biggest thing to worry about is Election Day. … It'd be pretty scary to try and go vote and have hundreds of people screaming at you about these ideas."

The Proud Boys were founded in 2016 by Vice magazine co-founder Gavin McInnes, who has since distanced himself from the group. They say they are a "fraternal group spreading an 'anti-political correctness' and 'anti-white guilt' agenda," according to the Southern Poverty Law Center. The group is suing the Southern Poverty Law Center over the characterization.

The group has been involved in a large neo-Nazi rally in Charlottesville, Va., in 2017, in the protests demonstrating against coronavirus lockdowns earlier this year and recent protests in Portland, Ore. Facebook has banned it, labeling it a hate group.

After operating on the political fringes for several years, the Proud Boys have recently made a push for more mainstream acceptance.

For many members, the president's remark was just the boost they craved, lending a new sense of purpose and legitimacy to their violent tactics and translating almost instantaneously into a recruitment drive.

"Acknowledgment from the top sets the pretense for increased white vigilantism," said Joan Donovan, director of the Technology and Social Change Research Project at Harvard University's Shorenstein Center. "This is a group that has organized street brawls using social media, has targeted people in their homes, and now believes their crusade against protesters is legitimate."