President Donald Trump on Tuesday didn't condemn white supremacist groups and their role in violence in some American cities this summer, branding it solely a "left-wing" problem and telling one far-right extremist group to "stand back and stand by."

"Almost everything I see is from the left wing, not from the right wing," said Trump, whose exchange with Democrat Joe Biden left the extremist group Proud Boys celebrating what some of its members saw as tacit approval.

He was responding to a question from debate moderator Chris Wallace, who asked the president if he would condemn white supremacist and militia groups that have showed up at some protests. Wallace specifically mentioned Kenosha, Wisconsin, where a white teenager was charged with killing two protesters during demonstrations over the police shooting of Jacob Blake, a Black man. Trump has repeatedly blamed "antifa," which stands for the anti-fascist movement.

"I'm willing to do anything. I want to see peace," Trump said. "What do you want to call them? Give me a name."

"Proud Boys," Democrat Joe Biden chimed in, referencing a far-right extremist group that has shown up at protests in the Pacific Northwest. The male-only group of neo-fascists describes themselves as "western chauvinists," and they have been known to incite street violence.

"Proud Boys, stand back and stand by," Trump said. "But I'll tell you what, I'll tell you what, somebody's got to do something about antifa and the left because this is not a right-wing problem."

FBI Director Christopher Wray told a congressional panel last week, though, that white supremacists and anti-government extremists have been responsible for most of the recent deadly attacks by extremist groups within the U.S.

Trump, a Republican, has tried to tie incidents of violence that have accompanied largely peaceful protests to Biden and the Democrats, running on a "law and order" message that warns people won't be safe under a Democratic president. It's a message aimed squarely at white suburban voters, including women who voted for Trump in 2016 but may not do so again. 

"What we saw was a dog whistle through a bullhorn," California Sen. Kamala Harris, Biden's running mate, said on MSNBC after the debate. "Donald Trump is not pretending to be anything other than what he is: Someone who will not condemn white supremacists."

Proud Boys leaders and supporters later celebrated the president's words on social media. A channel on Telegram, an instant messaging service, with more than 5,000 of the group's members posted "Stand Back" and "Stand By" above and below the group's logo.

Biden has said he decided to run for president after Trump said there were "very fine people" on both sides of a 2017 protest led by white supremacists in Charlottesville, Virginia, where a counterprotester was killed. 

Trump said Tuesday that Biden was afraid to say the words "law and order" and pressed him to give examples of law enforcement groups that back his campaign. Biden didn't name any, but said he's in favor of "law and order with justice, where people get treated fairly." 

Biden called antifa "an idea, not an organization." That's similar to how Wray described it, though Trump has called on the federal government to characterize antifa as a terrorist organization. 

At another point in the debate, when discussing a Trump administration move to end racial sensitivity training in the federal government, Biden directly called Trump a racist. He also accused him of trying to sow racist hatred and racist division in the country.