US President Donald Trump has reacted to widespread criticism following his failure to condemn outright a far-right group during his acrimonious debate with Democrat Joe Biden, saying The Proud Boys should “stand down”.

Mr Trump’s initial refusal to criticise the group – he initially said they should “stand back and stand by” – attracted fierce condemnation before he altered his message in an effort to quell the firestorm.

“I don’t know who Proud Boys are. But whoever they are they have to stand down, let law enforcement do their work,” Mr Trump told reporters as he left the White House for a campaign stop in Minnesota.

Proud Boys members had earlier revelled in the President’s debate comments, characterising them as “historic” and an endorsement.

Leaders and supporters of the group took to social media to celebrate the President’s words, with more than 5,000 of the group’s members posting “Stand Back” and “Stand By” above and below the group’s logo.

Mr Trump went on to call out forces on the other end of the political spectrum and tried to attack Mr Biden. It was an echo of the way he had blamed “both sides” for the 2017 violence between white supremacists and anti-racist protesters in Charlottesville, Virginia.

“Now antifa is a real problem,” Mr Trump said. “The problem is on the left. And Biden refuses to talk about it.”

In fact, FBI Director Christopher Wray told a congressional panel last week that it was white supremacists and anti-government extremists who have been responsible for most of the recent deadly attacks by extremist groups in the US

When Mr Trump was directly asked Wednesday if he “would welcome white supremacist support,” he ignored the question and again stressed the need for “law and order.”

The President has rarely condemned white supremacists when not pressed to do so, and his refusal to criticise the fascist group was denounced by Democrats on Wednesday.

“My message to the Proud Boys and every other white supremacist group is cease and desist,” Mr Biden said during a post-debate train tour through Ohio and Pennsylvania. “That’s not who we are. That’s not who we are as Americans.”

Senate Democratic Leader Chuck Schumer pressed his Republican colleagues: “How are you not embarrassed that President Trump represents your party? How can you possibly, possibly, support anyone who behaves this way?”

Meanwhile the group managing the US presidential election debates is planning steps to bring order to the remaining debates after widespread criticism.

The 90-minute debate on Tuesday night (local time) was chaotic, marred by the president’s constant interjections and interruptions of both his Democratic rival and the host, as well as Biden’s angry rejoinders.

The Commission on Presidential Debates, a nonpartisan group that has organised the events since 1988, said it would make unspecified changes to the format to prevent chaos.

“Last night’s debate made clear that additional structure should be added to the format of the remaining debates to ensure a more orderly discussion of the issues,” the group said in a statement on Wednesday.

Mr Biden said in a campaign stop on Wednesday that he hoped organisers of future debates would be able to turn off the microphone of the candidate who is not speaking.

“It was a national embarrassment,” Mr Biden said of the debate and Mr Trump’s performance.

Mr Trump, meanwhile, was critical of the debate’s moderator, Fox News anchor Chris Wallace.

“Chris had a tough night,” Mr Trump posted on Twitter on Wednesday morning, calling the debate a “two on one” fight.

Tweet from @realDonaldTrump

The debate commission defended Mr Wallace, thanking him “for the professionalism and skill he brought to last night’s debate” and promising “additional tools to maintain order”.

-with agencies