Charlie Kirk's alleged killer is "not co-operating" with authorities and has not confessed to carrying out the shooting, Utah's governor Spencer Cox has told US media.

Suspect Tyler Robinson, 22, was taken into custody some 33 hours after Kirk, a 31-year-old right-wing activist, was shot dead in Orem on Wednesday.

Speaking to ABC News, Cox, a Republican, said people around Mr Robinson had been co-operating with the investigation.

Cox appeared on various US news outlets on Sunday morning, where he also reiterated concerns regarding social media in the aftermath of Kirk's death.

The governor was also asked about a New York Times report alleging Mr Robinson had spoken to others after the shooting via the Discord messaging platform, including allegations that he joked about being the gunman.

Cox told ABC News: "All we can confirm is that those conversations definitely were happening, and they did not believe it was actually him.

"It was, it was all joking until, until he, you know, until he admitted that it actually was him."

Mr Robinson was arrested on Thursday night after surrendering to police.

Kirk was speaking at Utah Valley University at an open-air event held by Turning Point USA - the organisation he co-founded - when he was shot and killed.

The event was part of the American Comeback Tour, which was a speaking engagement that took him to several college campuses throughout the US.

Cox previously told the Wall Street Journal that Mr Robinson, a Utah native, was "deeply indoctrinated with leftist ideology".

When questioned on it during CNN's State of the Union programme on Sunday, he said the information was offered by the suspect's friends and family.

"There's so much more that we're learning and so much that we will learn," he explained, adding that when official charges are filed, there will be "much more evidence and information available then".

The governor said among those co-operating with authorities is Mr Robinson's roommate, who he said was also his partner.

He said the partner did not have have any knowledge about the alleged shooting, had been "incredibly co-operative" and was working with investigators "right now".

He also confirmed that the partner was currently "transitioning from male to female", but, when asked by CNN, said that authorities do not yet know if that is relevant to the investigation.

An affidavit from the state of Utah confirms that Mr Robinson was arrested on suspicion of the crimes of aggravated murder, felony discharge of a firearm, and obstruction of justice.

He is currently being held without bail at Utah County Jail.

"We're interviewing all kinds of people - everyone that knows him - and trying to learn more about what the motive actually was," Cox said.

Following Kirk's death, Cox has been prominent in calling for unity in a bid to ease political tensions, and has made repeated comments criticising social media.

He previously called social media a "cancer" and told CNN the US had "to get phones out of the classrooms" and better efforts to hold platform owners to account.

He called Kirk's shooting a "direct assault on America" and said Americans needed to "look in the mirror and decide, are we going to try to make it better, or are we going to make it worse?"