Media, citing police, reported that at least 11 people were injured.
Sixteen people were arrested, Officer Jennifer Coats of the Berkeley Police Department told the Times.
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"There continues to be a number of large fights, some property damage and numerous projectiles being thrown, including fireworks", police announced. Police said also that there have been numerous reports of pepper spray being used in the crowd.
The trouble unfolded when hundreds of Trump opponents staged a counter-rally alongside an event billed as a "Patriots Day" free-speech rally and picnic, which was organised by mostly Trump supporters.
Pro-Trump demonstrators, many from out of town, called for free speech, chanting "put America first". Officers confiscated knives, flagpoles, helmets and sticks with signs on them, things that were being used as weapons.
In another altercation, a protester who stole a Trump flag was chased down in front of a store and punched, until allies ran to his side and started to beat the Trump supporter involved.
Among those taking part in the counter-demonstration were black-clad Antifa activists, while on the pro-Trump side were members of the Oath Keepers militia from Montana, as well as a group of bikers.
"They hit me twice while I was down, it was sad", David Fry, also from Washington and pro-Trump, said.
Demonstrators have left the park and are walking on Berkeley streets while police closely follow them. Democratic Rep. Maxine Waters, of California, said there's nothing to prevent Trump from releasing his income taxes and that "the simple truth is he's got a lot to hide".
One of the injured was stabbed. A Berkeley station for BART, the mass transit system, was shut down because of the riots and police forces ended up using pepper spray on the crowd.
The police said more arrests could follow after videos shot during the melee were reviewed.
According to The Southern Poverty Law Center, which monitors and reports on American hate groups, Damigo - a former corporal in the U.S. Marine Corp - founded Identity Evropa in March of 2016, two years after his release from prison.
"We must become like them", she said referring to her opponents, "subversive".
Thousands protested at the University of California, Berkeley after alt-right Milo Yiannopolous was invited to speak on campus.
There were roughly 1,500 people at the dueling rallies.