The man arrested in the killing of right-wing activist Charlie Kirk is not cooperating with authorities, but investigators are working to establish a motive for the shooting by talking to his friends and family, Utah Governor Spencer Cox said on Sunday.

Cox said the accused gunman, Tyler Robinson, 22, would be formally charged on Tuesday. He remains in custody in Utah.

Investigators have yet to piece together why Robinson allegedly scaled a rooftop at Utah Valley University during an outdoor event and shot Kirk in the neck at long range on Wednesday.

Kirk, a staunch ally of President Donald Trump and co-founder of the conservative student group Turning Point USA, was killed by a single rifle shot during the event attended by 3,000 people in Orem, about 65 kilometres south of Salt Lake City.

The killing ushered in newfound fears of a spike in political violence in the United States and an ever-deepening divide between the left and the right.

RTHK's US correspondent, Mark Niu, said Kirk's death "shook the country to its core" and dominated conversations over the past few days.

"Even people that didn't know much about him find themselves digging for more information about him and going through a range of feelings involving empathy, rage and sadness that political differences have come to this," he told RTHK's Hong Kong Today.

"There's a certain sense that people are exhausted of the division in the country and bitterness in politics."

Robinson has not confessed to investigators, Cox told the ABC program "This Week."

"He is not cooperating, but all the people around him were cooperating, and I think that's very important," the Republican governor said.

One person who is apparently talking to investigators is Robinson's roommate, who was also a romantic partner, Cox said, citing the FBI.

Cox described the roommate as "a male transitioning to female," and said the roommate has been "incredibly cooperative."

Asked on CNN's "State of the Union" program whether the roommate's gender identity is relevant to the investigation, Cox said, "That's what we're trying to figure out right now ... It's easy to draw conclusions from that, and so we've got the shell casings, other forensic evidence that is coming in - and trying to piece all of those things together."

Investigators found messages engraved into four bullet casings, which included references to memes and video game in-jokes.

An affidavit filed by authorities in the case described these messages. One of the inscriptions, according to the affidavit, read: "hey fascist! CATCH!" followed by a combination of directional arrows, an apparent reference to a sequence of button presses that unleashes a bomb in a popular video game.

Another casing, according to the affidavit, read, "If you read This, you are GAY Lmao".

Kirk's charged rhetoric, which often involved anti-LGBT and anti-immigrant comments, attracted legions of conservatives, but also engendered strong feelings from liberals and drew widespread criticism.

Robinson, a third-year student in the electrical apprenticeship program at Dixie Technical College, part of Utah's public university system, was taken into custody at his parents' house, about 420 km southwest of the crime scene after a 33-hour manhunt.

Relatives and a family friend alerted authorities that he had implicated himself in the crime, Cox said previously.

While Robinson was raised by religious parents in a deeply conservative region of the state, "his ideology was very different than his family," Cox said on Sunday on NBC's "Meet the Press" program, without going into specifics.

State records show Robinson was a registered voter but not affiliated with any political party. A relative told investigators that Robinson had grown more political in recent years and had once discussed with another family member their dislike for Kirk and his viewpoints, according to the arrest warrant affidavit.

Robinson was "not a fan" of Kirk's, Cox said on Sunday.

The killing has stirred outrage among Kirk's supporters and condemnation of political violence from some across the ideological spectrum.

Many Republicans, including Trump, have been quick to lash out at the political left, accusing liberals of fomenting anti-conservative vitriol that would encourage violence - even as the president and his allies have often invoked violent imagery against their opponents.

"The problem is on the left," Trump told reporters on Sunday. "A lot of people that you would traditionally say are on the left ... (are) already under investigation." (Reuters/RTHK)