Leaving the White House for campaign appearances in Minnesota, Trump told reporters he doesn't know who the "Proud Boys" are -- despite having told the far-right group, which reportedly has described itself as "Western chauvinist" but not white supremacist, to "stand back and stand by" at the debate.
"I don't know who the Proud Boys are. I mean, you'll you 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 of the group which has staged counter protests in cities like Portland that have experienced recent violence.
But asked directly on Wednesday if he would denounce white supremacy, Trump claimed he has always denounced it -- yet once again didn't use the words "white supremacy."
"I've always denounced -- any form, any form, any form of any of that -- you have to denounce," Trump said.
A White House spokesperson had said earlier in the day there was nothing for the president to "clarify."
At Tuesday's debate, asked by moderator Chris Wallace of Fox News whether he was "willing to condemn white supremacists and militia groups and to say that they need to stand down and not add to the violence," the president at first said, "Sure, I'm willing to do that."
When Wallace pressed him, the president asked, "What do you want to call them?"
"White supremacists and right-wing militias," Wallace said, as former Vice President Joe Biden interjected the name "Proud Boys."
"Proud Boys, stand back and stand by," Trump then replied. "But I'll tell you what, somebody has got to do something about antifa and the left because this is not a right-wing problem. This is a left-wing problem."
The group reportedly has reportedly previously denied links to white supremacy or violence.
The Proud Boys describe themselves as "a pro-Western fraternal organization for men," according to the New York Times, and have denied they are part of the "alt-right" -- but members have recently been connected to white supremacist groups.
The primary organizer of the Unite The Right rally in Charlottesville, Virginia -- where one counter-protester was killed -- in 2017 was a former Proud Boys member, according to the Anti-Defamation League.
The group has reportedly previously denied accusations of being white supremacists.
Trump's debate response has drawn criticism from even his GOP allies in Congress.
Asked on Wednesday morning if he found the president's comments concerning, GOP Sen. Tim Scott of South Carolina -- the only African American Republican in the Senate -- suggested the president misspoke and should "correct it."
"I think he misspoke in response to Chris Wallace's comment. He was asking Chris what he wanted to say. I think he misspoke. I think he should correct it," Scott told Capitol Hill reporters.
"If he doesn't correct it, I guess he didn't misspeak," he added.
Usually a reliable supporter of the president, Scott played a prominent role at the Republican Convention last month in defending Trump, including on the issue of race. Nearly every time the president is asked about the African American community, he invokes Scott's name.
Senate Majority Leader Mitch McConnell, asked directly if it's a problem that the president did not directly condemn white supremacy, said he agreed with Scott's criticism, calling Trump's failure "unacceptable."
"With regard to the white supremacy issue I want to associate myself with the remarks of Senator Tim Scott that he put out earlier today. I think he said it exactly correctly and that's exactly how I would express myself on that issue," McConnell said. "He said it was unacceptable not to condemn white supremacists. and so I do so in the strongest possible way."
Sen. Lindsay Graham, another close ally of Trump's, also aligned himself with Scott's statement via Twitter.
"I agree with @SenatorTimScott statement about President Trump needing to make it clear Proud Boys is a racist organization antithetical to American ideals," he wrote.
Biden, asked on Wednesday at a campaign stop in Alliance, Ohio, if he has own message to the Proud Boys, made his views on white supremacy clear.
"My message to the Proud Boys and every other white supremacist group is cease and desist. That's not who we are. This is not who we are as Americans," Biden said.
"The American people will decide who the next president will be, so I urge the American people to go out and show up," he said, calling the debate a "wake up call" for the country.
Sen. Mitt Romney of Utah -- the only Republican who voted to convict Trump during his impeachment trial -- said "of course, of course" when asked on Capitol Hill Wednesday if the president should have outright condemned white supremacy.
"I'm not a political pundit and so I can't tell you what impact that will have," Romney said when asked about Trump's comment. "I can say I watched the debate last night. It was not a Lincoln-Douglas debate, that's for sure."
Republican Sen. Mike Rounds of South Dakota added that Trump should have been "very clear."
"He should have made it very clear that there's no room for people on the far left or the far more far right. When it comes to either antifa or these white supremacist groups, should have been very clear," Rounds said.
In a hearing on the Russia investigation on Capitol Hill Wednesday, former FBI Director James Comey said Trump's comments raise serious alarms about the security implications and the potential that it incites racist followers of such groups to commit acts of violence or recruit more members.
"The FBI is fighting a fire of racist violence, and with words like that the president is using a fire hose to spray gasoline on that fire," Comey said. "Maybe he misspoke, maybe when he said stand down and stand by he meant something else. I sure hope for the sake of our whole country he'll say that today, what he really meant and condemn these groups."
Outside Washington, the former Republican governor of Pennsylvania and the first U.S. secretary of Homeland Security, Tom Ridge, took to Twitter Wednesday to express his dismay.
"If a Republican President is incapable of condemning white supremacists, then the party of Lincoln has expired," Ridge wrote. Trump often compares himself to President Abraham Lincoln.