US President Donald Trump denounced white supremacist groups on Monday, two days after a white-nationalist rally turned deadly in Virginia, and earned him wide criticism for failing to respond more forcefully earlier.

"Racism is evil, and those who cause violence in its name are criminals and thugs, including the KKK, neo-Nazis, white supremacists and other hate groups that are repugnant to everything we hold dear as Americans," the president said at the White House on Monday.

"We condemn in the strongest possible terms this egregious display of hatred, bigotry and violence," the president said in a statement.

A 20-year-old man said to have harbored Nazi sympathies was arrested on charges of plowing his car into protesters opposing the white nationalists, killing 32-year-old paralegal worker Heather Heyer and injuring 19 other people in Charlottesville on Saturday, The Associated Press reported on Monday.

The accused, James Fields, was denied bail at a court hearing on Monday, according to the report.

Although the weekend event was triggered by the planned removal of a statue of Confederate Civil War General Robert E. Lee, the deep-rooted cause is the ever-increasing demographic changes in the US, which has ratcheted up the sense of crisis among traditional white Americans, Song Luzheng, a researcher with the China Institute of Fudan University in Shanghai, told China Daily.

"This increased sense of crisis of the whites has provided new ground for white supremacist and neo-Nazis groups to grow," he said in a written interview.

Zhang Xiping, dean of Academy of Comparative Civilizations and Intercultural Communication of the Beijing Foreign Studies University, said that historically, racism has been an issue that has not been "well resolved" in the US, which would lead to outbreaks of violence.

"The fact that there even was a white supremacist rally speaks to the way racism has festered in this country from the time the first slaves were transported here from Africa to now," said Camille Busette, a senior fellow of the Brookings Institution.

Thousands of protesters gathered outside Trump Tower in New York on Monday. Some protesters said they participated in the protest through Facebook pages. A Facebook page called Protest Donald Trump for the protest had a list of more than 4,900 planned attendees, and 17,000 people said they were interested in attending.

Protesters in the street were shouting "Hey! Hey! Ho! Ho! Donald Trump has got to go!" "No Trump, no KKK, no fascist USA." "Not my president!" and "Love, not hate, will make America great."

Others held signs reading: "Too little. Too Late!" in reference to President Trump's initial criticism of violence "on many sides".

The protests also reached the public library and 58th Street from Sixth Avenue to Madison Avenue, and 55th Street from Fifth Avenue to Madison Avenue were closed.

"I am here because I am disgusted by white supremacy in America. I don't feel like I have a lot of power except my voice and showing up in numbers," said Molly McCarthy, 32, a stage manager in New York.

"I am pretty horrified by what happened in Virginia. But sadly I am not shocked by it, because I know there is racism all over America," said Brooke Self, 27, a legal assistant who works in California.

"I think for those who are affected by racism it is important to hear that there are people against the extremist. We are here to demonstrate how important it is," Self said.

"I am furious at the Trump administration; I am furious at the way they have taken the values of this country and New York City, and turned their back on them," said Alex Lencicki, 43, a New Yorker who works in marketing.