US President Donald Trump has again blamed both sides for the violent unrest in Charlottesville, Virginia, which left one protester dead and others injured.
In a statement on Monday, he had condemned white supremacists.
But in New York on Tuesday he also blamed left-wing supporters for charging at the “alt-right”.
His latest comments drew swift criticism, including from some prominent Republicans.
Senator John McCain, a frequent critic of Mr Trump, tweeted: “There is no moral equivalency between racists & Americans standing up to defy hate & bigotry”.
The right-wing march had been organised to protest against the proposed removal of a statue of General Robert E Lee, who commanded the pro-slavery Confederate forces during the American Civil War. The event drew white supremacy groups.
Violence broke out after they were confronted by anti-racism groups. A car ploughed into one group of anti-racism protesters, killing 32-year-old Heather Heyer and 19 others.
Speaking at the White House on Monday, the US president had said that the Ku Klux Klan, neo-Nazis and white supremacists were “repugnant” to everything Americans held dear.
At a bad-tempered press conference at Trump Tower on Tuesday, Mr Trump called the car driver a disgrace to himself and his country but said that those who had marched in defence the statue had included “many fine people”.
He asked whether statues of former presidents George Washington and Thomas Jefferson should also be torn down, because they had been slave-owners.
“When you say alt-right…” Mr Trump said in an exchange with a reporter, using a term for right-wing groups.
“Okay, what about the alt-left that came charging at… the alt-right? Do they have any semblance of guilt? What about the fact that they came charging… with clubs in their hands?”
Mr Trump’s remarks were welcomed by David Duke, a former leader of the Ku Klux Klan, who tweeted: “Thank you President Trump for your honesty & courage to tell the truth about #Charlottesville & condemn the leftist terrorists in BLM/Antifa.”
But others strongly condemned the comments.
Republican Speaker Paul Ryan tweeted: “We must be clear. White supremacy is repulsive… there can be no moral authority.”
Florida Senator Marco Rubio said the organisers of the march were “100% to blame”.
Richard Trumka, president of the AFL-CIO trade union federation, resigned from President Trump’s American Manufacturing Council saying he could not take part “for a president who tolerates bigotry and domestic terrorism”.
“Charlottesville violence was fuelled by one side: white supremacists spreading racism, intolerance and intimidation. Those are the facts,” tweeted Virginia Democratic Senator Tim Kaine.
In another development, the response of former President Barack Obama to the violence in Charlottesville has become the most-liked tweet ever.
The message, quoting Nelson Mandela, reads: “No-one is born hating another person because of the colour of his skin or his background or his religion.”
It has been “liked” nearly three million times since being posted on Sunday.
In his address, Mr Trump defended the time it took to make his statement, saying he wanted to establish all the facts, and he again rounded on journalists at the news conference, saying many of them were writing “fake news”.
He also praised Ms Heyer’s mother, Susan Bro, who had thanked him after his earlier statement for his “words of comfort and for denouncing those who promote violence and hatred”.