A person was critically injured after a shooting "possibly associated" with a demonstration in downtown Salt Lake City, police said.

A person of interest in the shooting is in custody. The victim was taken to the hospital with life-threatening injuries, police said.

The shooting happened not far from Salt Lake City's Pioneer Park where a large crowd, estimated to be 10,000, had gathered for a march, according to police.

"The shooting at tonight’s protest in Salt Lake City is a deeply troubling act of violence and has no place in our public square," Utah Gov. Spencer Cox said in a social media post. "This is an active situation, and we’re working closely with law enforcement to ensure accountability."

Ahead of the planned curfew set to go into effect at 8 p.m. local time, the Los Angeles Police Department asked all demonstrators to leave the Civic Center area of downtown LA.

Shortly before the request, the LAPD said officers had requested assistance due to "agitators" throwing objects at officers.

Earlier, a dispersal order had been issued for an area of downtown after the LAPD said people in the crowd were throwing rocks, bricks and bottles.

The LAPD alleged on X that protesters at Temple and Spring streets threw "concrete, rocks, bottles and commercial grade fireworks at officers."

Protesters and media were advised to leave that area.

The LAPD and other agencies are aggressively clearing the streets of downtown LA, where protestors had pushed up against police lines.

Crowds were pushed away from the federal building by police, some of whom were on horses.

Officers fired less lethal munitions and a type of gas.

-ABC News's Alex Stone

Sixty demonstrators, part of a veterans protest against militarism, were arrested at the Supreme Court on Friday night and will be charged with unlawful demonstration and crossing a police line, Capitol police said. Some will also be charged with assault on a police officer and resisting arrest, police said.

"A few people pushed the bike rack down and illegally crossed the police line while running towards the Rotunda Steps," Capitol police said in a statement.

Brittany Ramos DeBarros, a former Army captain who was one of the organizers of the event, told ABC News that although they planned this before the protests in Los Angeles, they now also plan on calling attention to the Trump administration's deployment of the military to the LA protests.

“We need to see more courage, more resistance, to the terrifying consolidation of authoritarianism that we're seeing right now, particularly as we're seeing the Marines be mobilized in our own cities,” Ramos DeBarros said.

“It's not an accident that Trump is about to have tanks rolling down our streets here in D.C. [at Saturday’s Army anniversary parade] while he has the military also terrorizing immigrants in LA,” she said.

-ABC News’ Beatrice Peterson