Others did not mention Trump directly but did condemn the marchers, many of whom carried Nazi flags and similar regalia.
Trump did not mention white nationalists in his statement - and he reportedly ignored questions from the press about a auto plowing into multiple counter-protesters. As some counterprotesters began to disperse, a vehicle appeared on a street that at least some demonstrators had believed was blocked off to traffic.
Also Saturday, two Virginia State Police troopers were killed when a police helicopter went down seven miles southwest of Charlottesville shortly before 5 p.m., the Federal Aviation Administration and a senior law enforcement source briefed on the matter said.
Mr Trump declined to blame either side but said "the hate and the division must stop" at a press conference addressing events in the city.
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The scenes in Virginia were similar to others that happened around far-right protests at Berkeley, California, and Portland, Oregon.
Police began evacuating the city's Emancipation Park after declaring those gathered there to be part of an "unlawful assembly". Authorities confirmed to CBS News at least four people were hurt from the crash, suffering from injuries ranging from minor to life-threatening.
Hours after violence between counter-protesters and white nationalists ensued, President Donald Trump released an official statement on Twitter, writing: "We ALL must be united & condemn all that hate stands for".
Several members of Congress urged the president to refer to violence in central Virginia with stronger language after the commander in chief decried the egregious display of hatred, bigotry and violence. He called for "a swift restoration of law and order and the protection of innocent lives". "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", Trump said at a previously scheduled event for veterans.
Trump tweeted earlier Saturday on the situation in Charlottesville, saying "there is no place for this kind of violence in America".
Traci Blackmon, a black woman who was inside the church in Charlottesville, Virginia, described the fear of those people inside.
"Go home", he said. "There was violence between protesters and counter protesters today".