A woman died and 19 people were injured when a car rammed a crowd of people opposing a far-right rally there.
The FBI has opened a civil rights investigation into the incident.
Earlier, street brawls erupted between white nationalists and counter-protesters.
Attorney General Jeff Sessions said "the violence and deaths in Charlottesville strike at the heart of
American law and justice.
"When such actions arise from racial bigotry and hatred, they betray our core values and cannot be tolerated."
Twenty-year-old James Fields from Ohio, the alleged driver of the car, is in detention on suspicion of second-degree murder.
In detail: A reckoning in Charlottesville
In addition to those injured in the car incident, the Charlottesville Police Department said 15 were wounded in other violence related to the far-right march.
Late in the afternoon, a Virginia State Police helicopter crashed in woodland south-west of the city, killing two police officers. The helicopter had been part of the operation to monitor the clashes.
The "Unite the Right" march was called to protest against plans to remove a statue of General Robert E Lee, who had fought for the pro-slavery Confederacy during the US Civil War.
'You are anything but a patriot'
Mr McAuliffe told a press conference: "I have a message for all the white supremacists, and the Nazis who came into Charlottesville today. Our message is plain and simple: Go home. You are not wanted in this great commonwealth. Shame on you. You pretend that you're patriots, but you are anything but a patriot.
"You came here today to hurt people. And you did hurt people. But my message is clear: We are stronger than you."
The governor, who is a Democrat, said he had spoken to President Trump, and twice urged him to begin a movement to bring people together.
He thanked the police and law enforcement officials, who he said had prevented "a much worse day", and praised the emergency services who helped the wounded.
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