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 many in his Republican party.
Many echoed Senator John McCain's view: "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 injuring 19 others.
Bucket of kerosene
Anthony Zurcher, BBC North America reporter
On Monday, Donald Trump's condemnation of the far-right came from advisers counselling him on what was politically necessary to defuse the growing storm following the Charlottesville violence.
On Tuesday, the president said what he really thought.
Although he initially explained away the delay in condemnations of white supremacists as necessary for him to gather "the facts" of the situation, the nature of the protests were quite evident by the evening before, when demonstrators chanting white supremacist slogans held a torchlight parade through Charlottesville.
In any regard, Mr Trump has shown little reluctance in jumping to conclusions about violent incidents when it appears Islamic extremism is at play.
Upon further questioning, it became clear that the president views the Charlottesville unrest as far from a one-sided affair. Mixed in among the white supremacists, he said, were some good, peaceful people protesting the removal of a statue (of a man who led an army against the US government). And there were plenty of violent individuals among the counter-protesters as well.
When the president on Saturday said there were "many sides" to blame, he meant it.
If Donald Trump's initial handling of the fallout from Charlottesville started a political fire, on Tuesday the president poured on a bucket of kerosene and danced around the flames.
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.
But at a bad-tempered press conference at Trump Tower on Tuesday, he reverted to blaming "many sides" for Saturday's violence.
"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," he said.
"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."
He called the driver of the car that ploughed into the anti-racism protesters a disgrace to himself and his country, but said that those who had marched in defence of 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.
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 many others strongly condemned the comments.
Of the reactions of some 55 Republican and Democrat politicians collected by the Washington Post, only the spokeswoman for the Republican National Committee, Kayleigh McEnany, expressed her support.
President @realDonaldTrump once again denounced hate today. The GOP stands behind his message of love and inclusiveness!— Kayleigh McEnany (@kayleighmcenany) August 15, 2017
Republican Speaker Paul Ryan tweeted: "We must be clear. White supremacy is repulsive... there can be no moral ambiguity."
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".
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".