BOSTON, Massachusetts - Thousands of left-leaning counter-protesters marched through downtown Boston on Saturday, chanting anti-Nazi slogans and waving signs condemning white nationalism ahead of a rally being staged by conservative activists, just a week after a Virginia demonstration turned deadly.

Police Commissioner William Evans said Friday that 500 officers -- some in uniform, others undercover -- would be deployed to keep the two groups apart on Saturday. Boston's Democratic mayor, Marty Walsh, and Massachusetts' Republican governor, Charlie Baker, both warned that extremist unrest wouldn't be tolerated in this city famed as the cradle of American liberty. 

Walsh said at a news conference Friday that the city has spoken to the Southern Poverty Law Center, which provided guidance on how to handle conflicts with white supremacists, CBS Boston reported.

Organizers of the midday event, billed as a "Free Speech Rally," have publicly distanced themselves from the neo-Nazis, white supremacists and others who fomented violence in Charlottesville on Aug. 12. A woman was killed at that Unite the Right rally, and scores of others were injured, when a car plowed into counter-demonstrators. 

Police confined the "Free Speech" rally to the Parkman Bandstand on Boston Common as they blocked off the massive protests, CBS Boston reports.

The Boston Police Department announced at 1:30 p.m. that the "Free Speech" rally had ended.

John Medlar of the Boston Free Speech Coalition, which organized the event, is a 23-year-old student at Fitchburg State College. He told CBS News correspondent DeMarco Morgan that his group will not tolerate hate speech.

"Reasonable people on both sides who are tolerant enough to not resort to violence when they hear something they disagree with, reasonable people who are actually willing to listen to each other, need to come together and start promoting that instead of letting all of these fringe groups on the left and the right determine what we can and cannot say," Medlar said.

Opponents feared that white nationalists might show up in Boston anyway, raising the specter of ugly confrontations in the first potentially large and racially charged gathering in a major U.S. city since Charlottesville. 

Events also were planned Saturday for Atlanta and Dallas. 

Counter-protesters from Black Lives Matter and other groups denouncing racism and anti-Semitism planned to march from the city's Roxbury neighborhood to the Common, and another group planned to rally on the steps of the Statehouse overlooking the sprawling park. 

The permit issued for Saturday's noon-2 p.m. event on Boston Common came with severe restrictions, including a ban on backpacks, sticks and anything that could be used as a weapon. 

The Boston Free Speech Coalition said on Facebook that it's not affiliated with the Charlottesville rally organizers in any way. 

"We are not associated with any alt-right or white supremacist groups," it said this week, insisting: "We are strictly about free speech." 

Black Lives Matter said Friday that members from around the U.S. planned to march Saturday in Boston. 

Walsh said the city would do whatever is necessary to head off violence initiated by either side. "If anyone gets out of control - at all - it will be shut down," he said. 

"We will not tolerate any misbehavior, violence or vandalism whatsoever," said Evans, Boston's top cop. 

Dating to 1634, Boston Common is the nation's oldest city park. The leafy downtown park is popular with locals and tourists and has been the scene of numerous rallies and protests for centuries.