The Utah governor, Spencer Cox, on Sunday told national talkshows that the man suspected of killing Turning Point USA executive director Charlie Kirk was living with and in a relationship with a person “transitioning from male to female” as investigators continue exploring a possible motive in the attack.

The Republican politician’s comments came four days after Kirk – a critic of gay and transgender rights – was shot to death from a distance with a rifle during an event at Utah Valley University while speaking with a student about mass shootings in the US and trans people. Nonetheless, Cox stopped short of saying that officials had determined the suspect’s partner’s alleged status was a factor in Kirk’s killing.

In comments to NBC’s Meet the Press, Cox said that Kirk’s accused killer, 22-year-old Tyler Robinson, was not cooperating with authorities. Yet authorities are gathering information from family members and people around him, Cox said.

Cox said that what investigators had gathered showed Robinson “does come from a conservative family – but his ideology was very different than his family”.

Citing the content of investigators’ interviews with people close to Robinson, Cox said “we do know that the [suspect’s] roommate … is a [partner] who is transitioning from male to female.

“I will say that that person has been very cooperative with authorities,” Cox remarked to Meet the Press host Kristen Welker, referring to the roommate. “And … the why behind this … we’re all drawing lots of conclusions on how someone like this could be radicalized. And I think that those are important questions for us to ask and important questions for us to answer.”

The governor did not elaborate on the evidence that investigators were relying on to establish Robinson’s relationship to his roommate with whom he shared an apartment in Washington county, Utah, about 260 miles from where Kirk was killed.

Robinson’s arrest was announced on Friday after he surrendered to authorities to end a two-day manhunt in the wake of the 31-year-old Kirk’s killing.

At the time of his arrest, Robinson was a third-year student in an electrical apprenticeship program at Dixie Technical College.

Utah records show both of his parents are registered Republicans who voted in the 2024 election that gave Donald Trump, their party’s leader, a second presidency. But publicly available information offers little if any insight into Robinson’s personal beliefs.

Cox made it a point to tell NBC that “friends that have confirmed that there was kind of that deep, dark internet … culture and these other dark places of the internet” where Robinson “was going deep”. The governor did not elaborate – though on Saturday, citing the work of law enforcement, he told the Wall Street Journal that “it’s very clear to us and to investigators that this was a person who was deeply indoctrinated with leftist ideology.”

On Sunday, in a separate interview, CNN’s Dana Bash asked Cox to elaborate on his comments to the Journal.

“That information comes from the people around him, from his family members and his friends – that’s how we got that information,” Cox told CNN. “There’s so much more that we’re learning, and so much more that we will learn.”

Bash also asked Cox whether the roommate’s status was relevant to the investigation and a potential motive. The governor replied, “That is what we are trying to figure out right now.”

“I know everybody wants to know exactly why, and point the finger,” Cox said. “And I totally get that. I do, too.”

Yet Cox said he had not read all interview transcripts compiled by investigators, “so I just want to be careful … and so we’ll have to wait and see what comes out.”

Cox said he expected the public would learn more when formal charges were filed against Robinson. The governor said he expected that to happen Tuesday.

During his CNN appearance, Cox also said that investigators were looking into a potential note left by Robinson.

Officials at the group chat app Discord recently said that they had identified an account on the platform associated with Robinson – but found no evidence that the suspect planned the incident on the platform.

The spokesperson for Discord did say that there were “communications between the suspect’s roommate and a friend after the shooting, where the roommate was recounting the contents of a note the suspect had left elsewhere”.

When asked about the note, Cox said that “those are things that are still being processed for accuracy and verification”. He suggested additional details about the note could be “included in charging documents”.

Members of both of the US’s major political parties on Sunday reiterated condemnations of Kirk’s killing and political violence in general.

“Every American is harmed by this – it’s an attack on an individual and an attack on a country whose entire purpose, entire way of being is that we can resolve what we need to resolve through a political process,” Pete Buttigieg, a Democrat who served as the US transportation secretary during Joe Biden’s presidency, said to Welker.

Republican US senator Lindsey Graham, meanwhile, told Welker: “What I’m asking everybody to do is not to resort to violence to settle your political differences.”