The Proud Boys - who have been called an "extremist group with ties to white nationalism" by the FBI - became one of the big talking points of Tuesday's chaotic debate.
Mr Trump was widely criticised for failing to explicitly condemn white supremacist groups in the debate, while his opponent Democrat challenger Joe Biden, did.
When pushed by the moderator, the president replied: "Proud Boys, stand back and stand by" and went on to blame recent violence in cities such as Portland on left-wing activists.
Enrique Tarrio, international chairman of the group, told Sky News he did not see the president's words as an endorsement of his group, and that Mr Biden had made a "crucial mistake" in naming them as racists.
"We've been called many names, but probably the most inaccurate name you can call us is white supremacists," he said.
Mr Tarrio added: "I'm a 'person of colour', I'm a brown person, I'm chairman of the organisation [and] I got voted in..."
He added: "I think it was a great moment that we were mentioned on stage... if we were recognised by anyone we were recognised by Biden."
He defended the Proud Boys as peaceful, pointing to their rally in Portland over the weekend - the Oregon city that has seen months of often violent protests over police brutality and racism since the killing of George Floyd.
"We've always done that - we did this in Portland - we stood back and stood by in Portland on the 26th, and we had a great event," he said.
"And basically I think what he [President Trump] meant was let the police do their job - which we have."
Just hours after the debate the president distanced himself from the group on Wednesday saying: "I really don't know who they are".
"They have to stand down. Let law enforcement do their work," the president added.
Mr Biden again accused the group of being racists, telling them: "My message to the Proud Boys and every other white supremacist group is: cease and desist.
"The American people will decide who the next president is. Period," he added.