A man who was shot at a protest against President Donald Trump in Utah's capital has died, police in the western US state said on Sunday.

Arthur Folasa Ah Loo, 39, was shot at the Salt Lake City "No Kings" protest on Saturday, one of hundreds of demonstrations held around the country, after a 24-year-old man brandished an AR-15-style semi-automatic rifle, the city's police department said on X.

A third person fired three rounds at the 24-year-old gunman, "one of which tragically struck" Ah Loo, the police statement said.

It added that the man carrying the AR-15-style rifle, identified as Arturo Gamboa, had been "arrested and booked into jail on a charge of murder."

The charges were preliminary and would need to be confirmed by prosecutors.

Salt Lake City Police Chief Brian Redd, speaking at a press conference on Sunday, said Gamboa did not fire his weapon.

The man who shot at Gamboa was wearing a high-visibility vest and was apparently affiliated with protest organizers. He has not been charged and was cooperating with police, Redd said.

Gamboa had no criminal history, according to Redd, who said that investigators were still in the initial phases of probing what his possible motivations were.

The United States has been in the grip of intense political polarization, particularly since the election of President Trump last year.

The shots at the protest on Saturday sent panic coursing through the crowd in Salt Lake City, and came hours after a Minnesota lawmaker was killed at her home, in an apparent politically motivated assassination.