The driver of the car was arrested after fleeing the scene, but the police did not identify him. Cellphone videos showed that the car bore Ohio license plates. Mr. Thomas said the case was being treated as a criminal homicide.
“It was probably the scariest thing I’ve ever seen in my life,” said Robert Armengol, who was at the scene reporting for a podcast he hosts with students at the University of Virginia. “After that it was pandemonium. The car hit reverse and sped and everybody who was up the street in my direction started running.”
The planned rally was promoted as “Unite the Right” and both its organizers and critics said they expected it to be one of the largest gathering of white nationalists in recent times, attracting groups like the Ku Klux Klan and neo-Nazis and movement leaders like David Duke and Richard Spencer.
Many of these groups have felt emboldened since the election of Donald J. Trump as president. Mr. Duke, a former imperial wizard of the Ku Klux Klan, told reporters on Saturday that the protesters were “going to fulfill the promises of Donald Trump” to “take our country back.”
Saturday afternoon, President Trump, speaking at the start of a veterans’ event at his golf club in Bedminister, N.J., again addressed what he described as “the terrible events unfolding in Charlottesville, Virginia.”
In his comments, President Trump condemned the bloody protests, but he did not specifically criticize the white nationalist rally and its neo-Nazi slogans beyond blaming “hatred, bigotry and violence on many sides.”
“It’s been going on for a long time in our country, it’s not Donald Trump, it’s not Barack Obama,” said Mr. Trump, adding that he had been in contact with Virginia officials. After calling for the “swift restoration of law and order,” he offered a call for unity among Americans of “all races, creeds and colors.”
The president came under criticism from some who said he had not responded strongly enough against racism and that he failed to condemn the white nationalists groups by name who were behind the rally.
Among the critics was the mayor of Charlottesville, Mike Signer. “I do hope that he looks himself in the mirror and thinks very deeply about who he consorted with during his campaign,” he said.
The turmoil in Charlottesville began with a march Friday night by white nationalists on the campus of the University of Virginia and escalated Saturday morning as demonstrators from both sides gathered in and around the park. Waving Confederate flags, chanting Nazi-era slogans, wearing helmets and carrying shields, the white nationalists converged on the Lee statue inside the park and began chanting phrases like “You will not replace us” and “Jews will not replace us.”
Hundreds of counterprotesters — religious leaders, Black Lives Matter activists and anti-fascist groups known as “antifa” — quickly surrounded the park, singing spirituals, chanting and carrying their own signs.
The morning started peacefully, with the white nationalists gathering in McIntire Park, outside downtown, and the counterdemonstrators — including Cornel R. West, the Harvard University professor and political activist — gathering at the First Baptist Church, a historically African-American church here. Professor West, who addressed the group at a sunrise prayer service, said he had come “bearing witness to love and justice in the face of white supremacy.”
At McIntire Park, the white nationalists waved Confederate flags and other banners. As a photographer took pictures, one of them, who gave his name only as Ted because he said he might want to run for political office some day, said he was from Missouri, and added, “I’m tired of seeing white people pushed around.”
But by 11 a.m., after both sides had made their way to Emancipation Park, the scene had exploded into taunting, shoving and outright brawling.
Barricades encircling the park and separating the two sides began to come down, and the police temporarily retreated. People were seen clubbing one another in the streets, and pepper spray filled the air. One of the white nationalists left the park bleeding, his head wrapped in gauze.
Declaring the gathering an unlawful assembly, the police had cleared the area before noon, and the Virginia National Guard arrived as officers began arresting some who remained. But fears lingered that the altercation would start again nearby, as demonstrators dispersed in smaller groups.
Within an hour, politicians, including Gov. Terry McAuliffe, a Democrat, and the House speaker, Paul D. Ryan of Wisconsin, a Republican, had condemned the violence.
The first public response from the White House came from the first lady, Melania Trump, who wrote on Twitter: “Our country encourages freedom of speech, but let’s communicate w/o hate in our hearts. No good comes from violence.”
Attorney General Jeff Sessions said Justice Department agents would support local and state officials in an investigation of Saturday’s events.
“This kind of violence is totally contrary to American values and can never be tolerated,” Mr. Sessions said in a statement.
After the rally was dispersed, its organizer, Jason Kessler, who calls himself a “white advocate,” complained in an interview that his group had been “forced into a very chaotic situation.” He added, “The police were supposed to be there protecting us and they stood down.”
Both Mr. Kessler and Richard Spencer, a prominent white nationalist who was to speak on Saturday, are graduates of the University of Virginia. In an online video, titled “a message to Charlottesville,’’ Mr. Spencer vowed to return to the college town.
“You think that we’re going to back down to this kind of behavior to you and your little provincial town? No,’’ he said. “We are going to make Charlottesville the center of the universe.”
The Charlottesville street fights were the latest in a series of tense dramas unfolding across the United States over plans to remove statues and other historical markers of the Confederacy. The battles have been intensified by the election of Mr. Trump, who enjoys fervent support from white nationalists.