White supremacists are celebrating online after Donald Trump's latest remarks addressing the Charlottesville rioting.

Mr Trump "went rogue" during a press conference about infrastructure at Trump Tower on Tuesday, a White House source told NBC, by taking questions on Saturday's violence in Virginia and repeating his belief that blame lay on "both sides".

He told reporters in New York during a sometimes heated exchange: "I have no doubt about it. You don't have doubt about it either."

Not everyone protesting against the removal of the city's statue of Confederate general Robert E Lee was a neo-Nazi, Mr Trump said, and that while "you had some very bad people in that group", there were also "some very fine people on both sides".

Ex-KKK leader David Duke praised the President for his "honesty and courage" while a Fox News clip of Mr Trump speaking was shared across far-right sections of Twitter, including by white nationalist blogger Hunter Wallace, who had joined the ranks of protesters on the day.

White supremacist leader Richard Spencer also retweeted the clip, while on alternative social media site Gab, users said Mr Trump "came through for us" and that "this is more like it", according to Think Progress. "I was fist-pumping!" said another.

Mr Spencer said: "Trump's statement was fair and down to earth. #Charlottesville could have been peaceful, if police did its job."

Footage from Saturday showed how the right-wing crowd gathered early in the day, with white nationalist groups armed with batons and shields forming ranks as they approached Emancipation Park.

Video also emerged of heavily armed militia groups filing through the Charlottesville streets carrying AR-15 assault rifles with spare ammunition, knives, radios and tactical clothing.

Violence on the streets of Charlottesville Show all 9 1 /9 Violence on the streets of Charlottesville Violence on the streets of Charlottesville Protesters clash and several are injured White nationalist demonstrators clash with counter demonstrators at the entrance to Lee Park in Charlottesville, Virginia. A state of emergency is declared, August 12 2017 Violence on the streets of Charlottesville Trump supporters at the protest A white nationalist demonstrator walks into Lee Park in Charlottesville, Va., Saturday, Aug. 12, 2017. Hundreds of people chanted, threw punches, hurled water bottles and unleashed chemical sprays on each other Saturday after violence erupted at a white nationalist rally in Virginia. AP Photo Violence on the streets of Charlottesville State police stand ready in riot gear Virginia State Police cordon off an area around the site where a car ran into a group of protesters after a white nationalist rally in Charlottesville, Virginia AP Photo Violence on the streets of Charlottesville Militia armed with assault rifles White nationalists, neo-Nazis and members of the 'alt-right' with body armor and combat weapons evacuate comrades who were pepper sprayed after the 'Unite the Right' rally was declared a unlawful gathering by Virginia State Police. Militia members marched through the city earlier in the day, armed with assault rifles. Getty Images Violence on the streets of Charlottesville Statue of Confederate General Robert E Lee The statue of Confederate General Robert E. Lee stands behind a crowd of hundreds of white nationalists, neo-Nazis and members of the 'alt-right' during the 'Unite the Right' rally 12 August 2017 in Charlottesville, Virginia. They are protesting the removal of the statue from Emancipation Park in the city. Getty Images Violence on the streets of Charlottesville Racial tensions sparked the violence White nationalists, neo-Nazis and members of the 'alt-right' exchange insults with counter-protesters as they attempt to guard the entrance to Lee Park during the 'Unite the Right' rally Getty Violence on the streets of Charlottesville A car plows through protesters A vehicle drives into a group of protesters demonstrating against a white nationalist rally in Charlottesville, Virginia. The incident resulted in multiple injuries, some life-threatening, and one death. AP Photo Violence on the streets of Charlottesville Rescue personnel help injured people after a car ran into a large group of protesters after an white nationalist rally in Charlottesville, Virginia AP Photo Violence on the streets of Charlottesville President Donald Trump speaks about the ongoing situation in Charlottesville, Virginia from his golf club in Bedminster, New Jersey. He spoke about "loyalty" and "healing wounds" left by decades of racism.

When violence did erupt, anti-fascist demonstrators faced off with members of several white nationalist groups, with pepper spray and other weapons used by both.

But it was counter-protesters who were victims in the most shocking violence of the day, when James Fields, 20, allegedly drove a car into their group, killing one and injuring several more.

Mr Trump had faced widespread criticism for his failure to condemn directly the racism on display at Charlottesville until two days afterward.

Charlottesville mayor: There's a 'direct line' between what happened here and Trump

He first denounced "violence on all sides" but issued a second statement on Monday.

He said: "No matter the color of our skin, we all live under the same laws, we all salute the same great flag, and we are all made by the same almighty God.

"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."

His fellow Republicans reacted swiftly after yesterday's statement.

House majority leader Paul Ryan said: "We must be clear. White supremacy is repulsive. This bigotry is counter to all this country stands for. There can be no moral ambiguity."