Washington DC - President Donald Trump urged supporters Thursday to respond peacefully to the killing of right-wing campaigner Charlie Kirk, as the murderer continued to evade a manhunt more than 24 hours after the shooting put an already divided US on edge.

Trump, who soon after the killing angrily pledged a wide-ranging response against the "radical left," told reporters that Kirk had been "an advocate of nonviolence."

"That's the way I'd like to see people respond," he said.

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Kirk, a 31-year-old superstar on the Republican right who sparked surging youth support for Trump, was shot while addressing a large crowd at Utah Valley University on Wednesday.

Trump cited "big progress" in the investigation.

However, authorities said the gunman remained at large a day later.

"Multiple leads are currently being investigated, but no suspect is in custody," Utah law enforcement officials posted, after canceling a previously scheduled media briefing.

"We're doing everything we can to find him, and we're not sure how far he has gone yet," FBI Special Agent Robert Bohls said earlier.

The FBI, which described the attack on Kirk as "targeted," published grainy photos of a young person it called "the potential shooter."

The pictures showed a man wearing a black baseball cap, dark sunglasses, and what appeared to be jeans, with a long-sleeved top emblazoned with a design that included an American flag.

A reward of up to $100,000 was posted for information leading to his capture.

Police say they believe the shooter fired a single bullet from a rooftop up to 200 yards, hitting Kirk in the neck.

A high-powered bolt-action rifle was recovered in a wooded area.