President Donald Trump's remarks condemning violence at a white nationalist rally were meant to include the Ku Klux Klan and neo-Nazi groups, the White House insisted on Sunday, a day after he was criticized by Republicans and Democrats for not explicitly denouncing white supremacists.

"The president said very strongly in his statement yesterday that he condemns all forms of violence, bigotry, and hatred, and of course that includes white supremacists, KKK, neo-Nazi, and all extremist groups. He called for national unity and bringing all Americans together." The statement was emailed to reporters covering Trump at his golf resort in New Jersey and attributed to an unidentified "White House spokesperson."

Trump, while on a working vacation at his New Jersey golf club, addressed the nation Saturday soon after a car plowed into a group of anti-racist counter-protesters in Charlottesville, a college town where neo-Nazis and white nationalists had assembled for a march. The president did not single out any group, instead blaming "many sides" for the violence.

Trump condemned "in the strongest possible terms this egregious display of hatred, bigotry and violence on many sides, on many sides," repeating the phrase for emphasis. He added: "It's been going on for a long time in our country. Not Donald Trump. Not Barack Obama. It's been going on for a long, long time."

That statement has drawn strong criticism.

APTOPIX Confederate Monuments Protest

The moment a vehicle is driven into a group of protesters demonstrating against the white supremacist rally in Charlottesville on Saturday is captured in this photo. (Ryan M. Kelly/The Daily Progress/Associated Press)

'Call evil by its name'

Colorado Republican Sen. Cory Gardner tweeted: "Mr. President — we must call evil by its name. These were white supremacists and this was domestic terrorism."

Added Sen. Marco Rubio, a Republican from Florida: "Nothing patriotic about #Nazis, the #KKK or #WhiteSupremacists It's the direct opposite of what #America seeks to be."

New Jersey Gov. Chris Christie, a Republican and staunch Trump supporter, wrote: "We reject the racism and violence of white nationalists like the ones acting out in Charlottesville. Everyone in leadership must speak out."

On the Democrat side, Senate Minority Leader Charles Schumer of New York said "of course we condemn ALL that hate stands for. Until @POTUS specifically condemns alt-right action in Charlottesville, he hasn't done his job."

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."

Car used as weapon in 'terrorist attack'

Charlottesville Mayor Mike Signer, appearing Sunday for an interview on NBC's Meet the Press, called the fatal car crash on Saturday a "terrorist attack with a car used as a weapon."

"People are dying and I do think that it's now on the president and on all of us to say 'enough is enough,'" Signer said.

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Rescue workers move victims on stretchers after a car plowed through a crowd of counter-demonstrators marching through the downtown shopping district of Charlottesville, Va. (Chip Somodevilla/Getty Images)

Trump's national security adviser, H.R. McMaster, said Sunday that he considered the attack in Charlottesville to be terrorism.

"I certainly think anytime that you commit an attack against people to incite fear, it is terrorism," McMaster told ABC's This Week.

"It meets the definition of terrorism. But what this is, what you see here, is you see someone who is a criminal, who is committing a criminal act against fellow Americans."

The president's homeland security adviser, Tom Bossert, defended the president's statement by suggesting that some of the counter-protesters were violent, too.

When pressed, he specifically condemned the racist groups. The president's daughter and White House aide, Ivanka Trump, tweeted Sunday morning: "There should be no place in society for racism, white supremacy and neo-Nazis."

James Alex Fields Jr. car composite

James Alex Fields Jr., 20, has been charged with second-degree murder, three counts of malicious wounding and one count related to leaving the scene in relation to a violent incident in which a car rammed counter-protesters. (Charlottesville Police Department/Reuters, Win McNamee/Getty)

The U.S. Justice Department opened a federal civil rights investigation after the vehicle struck anti-racist protesters Saturday while they rallied against white nationalists holding a "Unite the Right" rally. The rally drew a mix of white nationalists, far-right militias, alt-right supporters and extremist white supremacist groups like the KKK.

James Alex Fields Jr., 20, of Maumee, Ohio, faces several charges, including second-degree murder, in the attack, which killed Heather Heyer, a 32-year-old paralegal from Greene County, Va. A GoFundMe campaign that started Saturday for Heyer's family has already exceeded its $200,000 US goal.

​Police have not yet provided a motive for the car-ramming incident where 19 others were injured at the scene. In all, 35 people were hurt in the rallies. But U.S. attorneys and the Federal Bureau of Investigation have opened a civil rights investigation, an FBI field office said.

Confederate Monument Protest

Virginia State Police Trooper-Pilot Berke M.M. Bates, left, of Quinton, Va., and Lt. H. Jay Cullen, of Midlothian, Va., were killed Saturday when the helicopter they were piloting crashed while they were helping law enforcement officers monitor the white nationalist rally. (Virginia State Police/Associated Press)

Federal authorities were also looking into a helicopter crash on Saturday that killed two Virginia state police officers who were monitoring the clashes.

Virginia Gov. Terry McAuliffe, a Democrat, declared an emergency and halted the white nationalist rally planned for Saturday, but that did not stop the violence.

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Virginia Gov. Terry McAuliffe embraces one of the worshippers at the First Baptist Church in Charlottesville after speaking at morning services. (Win McNamee/Getty Images)

Rival groups fought pitched battles using fists, rocks and pepper spray. Three men were arrested in connection with the violence and face charges that include disorderly conduct, assault and carrying a concealed handgun.

'No place for you in America,' governor says

"Please go home and never come back," was Gov. McAuliffe's message for the white supremacists, delivered at a news conference Saturday.

"There is no place for you here, there is no place for you in America," he said.

McAuliffe repeated the message at a Charlottesville church on Sunday:

"To the white supremacists and neo-Nazis who came to our beautiful state yesterday, there is no place for you in Charlottesville. There is no place for you in Virginia. There is no place for you in the United States of America. We deplore your hatred and bigotry, and shame on you."

The planned rally stemmed from 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 slavery.

Jason Kessler, a right-wing blogger who organized what he termed the "pro-white" rally on Saturday, tried to hold a news conference in Charlottesville on Sunday near city hall.

But a crowd of several hundred booed and drowned him out with chants, drums and other instruments. He was eventually escorted away by state troopers after he was pushed and tackled by several people.

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Protesters objecting to the planned removal of a Civil War statue in Charlottesville clash with counter-protesters as they enter a park during a 'Unite the Right' rally on Saturday. Police declared it an unlawful gathering and people were forced out. (Chip Somodevilla/Getty Images)

The Charlottesville violence is the latest clash involving far-right groups, some of whom have claimed allegiance to Trump 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.

The protests at the University of Virginia on Friday night and those the following day involved supporters of the Ku Klux Klan, along with neo-Nazi groups.

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Charlottesville, Va., council voted in April to remove a bronze Robert E. Lee statue in a park that has been the site of far-right protests and Ku Klux Klan rallies, as well as counter-protests like this one, held on July 8. (Chet Strange/Getty Images)

They were objecting to Charlottesville's plans to remove a statue of the Confederate general Robert E. Lee from a downtown park. About two dozen people were arrested in Charlottesville in July when the Ku Klux Klan rallied against the plan to remove the Lee statue. Torch-wielding white nationalists also demonstrated in May against the removal.

Thousands of people turned out to rallies across the U.S. to denounce the violence in Charlottesville.

In Oakland, Calif., organizers distributed fliers with the slogan "Charlottesville, We Got Your Back."

There were rallies in several other cities, including New York, Boston and  San Francisco.

More solidarity protests were planned for Sunday in Washington state and Maryland. 

With files from CBC News and Reuters