"We're closely following the terrible events unfolding in Charlottesville, Virginia," Trump told reporters at his New Jersey golf course. "We condemn in the strongest possible terms this egregious display of hatred, bigotry and violence on many sides."
Trump made no reply to a reporter's shouted question whether he had spoken out strongly enough against white nationalists.
In a statement issued after the president's news conference, the White House defended Trump's use of "many sides," saying that he "was condemning hatred, bigotry and violence from all sources and all sides. There was violence between protesters and counter protesters today."
Prominent Democrats, civil rights activists and some Republicans said it was inexcusable of the president not to denounce white supremacy.
"Mr. President — we must call evil by its name," Republican U.S. Senator Cory Gardner wrote on social network Twitter.
"These were white supremacists and this was domestic," said Gardner, chairman of the National Republican Senatorial Committee, the group charged with helping to get Republicans elected to the Senate.
Nancy Pelosi, the Democratic leader in the U.S. House of Representatives, said in a tweet directed at the president: "Repeat after me, @realDonaldTrump: white supremacy is an
affront to American values."
Fighting broke out on Saturday in the city's downtown, when hundreds of people, some wearing white nationalist symbols and carrying Confederate battle flags, were confronted by a nearly equal number of counter-protesters.
The confrontation was a stark reminder of the growing political polarization since Trump's election last year.
"You will not erase us," chanted a crowd of white nationalists, while counter-protesters carried placards that read: "Nazi go home" and "Smash white supremacy."
Scott Stroney, 50, a catering sales director at the University of Virginia who arrived at the scene of the car incident just after the crash, said he was horrified.
"I started to cry. I couldn't talk for a while," he said. "It was just hard to watch, hard to see. It's heartbreaking."
The violence began on Friday night, when hundreds of white marchers with blazing torches appeared at the campus in a display that critics called reminiscent of a Ku Klux Klan rally.
David Duke, a former leader of the white supremacist Ku Klux Klan, was in Charlottesville for the rally, according to his Twitter account.
"We are determined to take our country back," Duke said in a video reportedly from the rally. "We are going to fulfill the promises of Donald Trump. That's what we believed in. That's why we voted for Donald Trump, because he said he's going to take our country back."
The rally was part of a long debate in the U.S. South over the Confederate battle flag and other symbols of the rebel side in the Civil War, which was fought over the issue of slavery.
The violence is the latest clash between far-rightists, some of whom have claimed allegiance to Trump, and the president's opponents since his January inauguration, when black-clad anti-Trump protesters in Washington smashed windows, torched cars and clashed with police, leading to more than 200 arrests.
—CNBC contributed to this report.