The Republican president -- who one day ago solemnly denounced racism and singled out the Ku Klux Klan and neo-Nazis as "criminals and thugs" -- also hit out at the "alt-left" over the weekend melee.
Trump has faced days of criticism from across the political spectrum over his reaction to Saturday's unrest in the Virginia college town, where a rally by neo-Nazis and white supremacists over the removal of a Confederate statue erupted in clashes with counter-demonstrators.
The violent fracas ended in bloodshed when a 20-year-old suspected Nazi sympathiser, James Fields, plowed his car into a crowd of anti-racism protesters, leaving one woman dead and 19 others injured.
In a rowdy exchange with journalists at Trump Tower in New York, Trump made clear on Tuesday that he was fed up with continued questioning about the issue.
"I think there is blame on both sides," Trump said.
"You had a group on one side that was bad, and you had a group on the other side that was also very violent. And nobody wants to say that, but I'll say it right now," Trump added.
"What about the alt-left that came charging... at the, as you say, the alt-right? Do they have any semblance of guilt? (...) There are two sides to a story."
'No words'
Trump's comments were immediately welcomed by David Duke, a former "grand wizard" of the Ku Klux Klan and a key figure at Saturday's rally.
"Thank you President Trump for your honesty & courage to tell the truth about #Charlottesville & condemn the leftist terrorists," Duke tweeted.
But on the political left, the president's words were met with indignation.
"Charlottesville violence was fueled by one side: white supremacists spreading racism, intolerance & intimidation. Those are the facts," said Tim Kaine, a former Democratic vice presidential candidate and senator from Virginia.
The state's other Democratic senator, Mark Warner, tweeted: "No words."
NBA superstar LeBron James tweeted: "Hate has always existed in America. Yes we know that but Donald Trump just made it fashionable again!"
After the contentious press conference, the head of the main US labor union, the AFL-CIO, joined several high-powered executives in stepping down from Trump's advisory panel on manufacturing.
"President Trump's remarks today repudiate his forced remarks yesterday about the KKK and neo-Nazis," union leader Richard Trumka said in a statement.
"We must resign on behalf of America's working people, who reject all notions of legitimacy of these bigoted groups."
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'Is it George Washington next week?'
When asked why he waited until Monday to explicitly condemn hate groups present in Charlottesville, Trump said he wanted to be careful not to make a "quick statement" on Saturday without all the facts.
"I wanted to make sure, unlike most politicians, that what I said was correct," Trump insisted.
Trump called Fields, who has been charged with second-degree murder, a "disgrace to himself, his family and this country."
But he also said that while there were troublemakers at the rally, there were also many people there "to innocently protest and very legally protest" the removal of a "very important statue" of Confederate general Robert E Lee.
"I wonder, is it George Washington next week? And is it Thomas Jefferson the week after?" he said angrily.
"Are we going to take down statues to George Washington? How about Thomas Jefferson?"
The president also used Tuesday's press conference to defend his controversial far-right chief strategist Steve Bannon, saying: "I like Mr Bannon. He's a friend of mine... He is a good man. He is not a racist."
Trump, however, did not rule out Bannon's departure from the West Wing, after The New York Times reported that media mogul Rupert Murdoch had urged him to dump the former head of ultra conservative outlet Breitbart News.
"We'll see what happens with Mr Bannon," Trump said.
