President Donald Trump has said a far-right group should "stand down" and let law enforcement do its work, after his refusal to explicitly condemn the group in a TV debate sparked a backlash.
Mr Trump said "I don't know who the Proud Boys are", a day after urging them in the election debate with Joe Biden to "stand back and stand by".
Proud Boys members called his debate comments "historic" and an endorsement.
Mr Biden said Mr Trump had "refused to disavow white supremacists".
The exchange came during the first of three televised debates between the two men ahead of the 3 November election. The debate descended into squabbling, bickering and insults, with US media describing it as chaotic, ugly and awful.
The commission that regulates the debates said it would introduce new measures for the next two to "maintain order". Mr Trump said they should get a new anchor and a smarter Democratic candidate.
Not much was gleaned on policy and although one snap poll on the debate gave Mr Biden a slight edge, other opinion polls suggest 90% of Americans have already made up their mind on who to vote for and the debate may well have made little difference.
Mr Biden has consistently led Mr Trump in national polls, but surveys in so-called battleground states suggest the vote could still be a close contest.
What did Mr Trump say about Proud Boys in the debate?
Moderator Chris Wallace asked whether the president would condemn white supremacists and tell them to stand down during protests. These have flared this year over the issues of police killings and racism.
"Sure, I'm willing to... but I would say almost everything I see is from the left wing, not from the right wing," Mr Trump said.
Mr Biden twice said "Proud Boys" when the president asked who it was he was being told to condemn.
The president said: "Proud Boys - stand back and stand by. But I'll tell you what... Somebody's got to do something about antifa and the left because this is not a right-wing problem."
Founded in 2016, Proud Boys is a far-right, anti-immigrant, all-male group with a history of street violence against left-wing opponents. One Proud Boys social media account posted the logo "Stand Back, Stand By."
Mr Biden was meanwhile accused by conservatives of downplaying the threat of antifa.
Antifa, short for "anti-fascist", is a loose affiliation of far-left activists that often clash with the far right at protests.
During the debate, Mr Biden quoted the FBI director as saying recently that antifa is "an idea, not an organisation".
The FBI director also said in his congressional testimony this month that antifa was a "movement" that includes "violent anarchist extremists".
The US Department of Justice has accused antifa of instigating violence linked to rioting in US cities this year.
How did Mr Trump clarify his debate comments?
He was speaking on the White House lawn on Wednesday ahead of a campaign trip to Minnesota. A reporter asked him about Proud Boys and he said: "I don't know who they are. I can only say they have to stand down and let law enforcement do their work."
He repeated his demand that Mr Biden condemn the activities of antifa.
He did not clarify his use of "stand by" in the debate and said only that he wanted "law and order to be a very important part of our campaign" when asked whether he welcomed white supremacist support.
Pressed again on the issue, he said: "I've always denounced any form, any form of any of that."
A Trump statement after a neo-Nazi killed an anti-white supremacy protester with his car in Charlottesville in 2017 did condemn "the KKK, neo-Nazis, white supremacists, and other hate groups". Mr Trump also said there were "very fine people on both sides" during those protests.
The Department of Homeland Security says white supremacy groups will remain the most "persistent and lethal threat" in the United States into next year.
When confronted with tough or tricky issues, Donald Trump has a tendency to offer a smorgasbord of often contradictory answers, allowing his supporters - and detractors - to pick and choose what to believe.
Nowhere has this behaviour been more pronounced than when he addresses white supremacists and extremist right-wing groups. At times he has renounced them. At others, he equivocates or changes the subject when a direct condemnation would suffice.
Instead, the president ends up offering a rallying cry to hate groups, as he did following the 2017 Charlottesville violence or with his "stand back and stand by" message on Tuesday.
The president can say all the right things politically, then turn around and say all the wrong things, leaving his aides to clean up the mess.
Is it because the president is careless with his words, misunderstood by critics and an adversarial press, or because he is sensitive to the concerns of even the more distasteful elements of his support base?
Despite all the talking and tweeting he does, the president - intentionally or not - remains a cypher.
What was the president accused of?
Joe Biden returned to the issue in a tweet on Wednesday, saying: "There's no other way to put it: the President of the United States refused to disavow white supremacists on the debate stage last night."
In his tweet he quoted a comment, addressed to the president, from a Proud Boys online forum that read: "This makes me so happy. We're ready! Standing by sir."
Anti-Defamation League CEO Jonathan Greenblatt said Mr Trump's words were "astonishing" and Rita Katz, of the SITE extremist watchdog, said Mr Trump had given "another nod to white supremacists".
Proud Boys members certainly believed they had been supported by Mr Trump.
Organiser Joe Biggs wrote: "President Trump told the proud boys to stand by because someone needs to deal with antifa... well sir! we're ready!!"
One member said the group was already seeing a spike in new recruits.
What were the other key debate moments?
The 90-minute debate in Cleveland, Ohio, was chaotic, with frequent interruptions and the men flinging insults at each other.
The main issues included:
- Among the insults, Mr Biden call the president a "clown". He told the president: "Will you shut up, man?" and later snapped "Keep yapping, man"
- Mr Trump said Mr Biden had "graduated either the lowest or almost the lowest in your class" and had done nothing in 47 years of politics
- Mr Biden said Mr Trump had "panicked" over the coronavirus epidemic and a "lot of people died". Mr Trump later tweeted that many more would have died if Mr Biden had been president
- Mr Trump defended his effort to swiftly fill a US Supreme Court seat, while Joe Biden refused to answer when asked if he would try to expand the number of judges
- When asked if he would encourage his supporters to be peaceful if results of the election were unclear, Mr Trump said: "I'm encouraging my supporters to go into the polls and watch very carefully"
- When Mr Trump said Mr Biden would be at the behest of the left of the Democratic Party over health and environmental policy, Mr Biden responded: "I am the Democratic Party right now"
What happens now?
The war of words following the debate lingered in exchanges on Wednesday.
On Twitter, Mr Trump said Mr Biden would destroy the country, claiming the challenger wishes to pack the Supreme Court with judges, end fracking and kill the Second Amendment of the Constitution, which includes the right to bear arms.
Nobody wants Sleepy Joe as a leader, including the Radical Left (which he lost last night!). He disrespected Bernie, effectively calling him a loser!— Donald J. Trump (@realDonaldTrump) September 30, 2020
Joe Biden is on an all-day train tour through eastern Ohio and western Pennsylvania, while his campaign has also rolled out a digital advert onslaught against the president.
He said on his first tour stop that Mr Trump had "forgotten the forgotten Americans he said he was going to fight for. I will never forget".
Mr Biden added: "I am not going to be a Democratic president. I am going to be an American president."
The other TV debates between the two candidates are on 15 October in Florida and 22 October in Tennessee.