DNA on a towel wrapped around the suspected gun used to kill Charlie Kirk has been matched to the suspect in custody, the director of the FBI said on Monday.

Tyler Robinson, 22, was arrested over the death of the right-wing influencer at an event at Utah Valley University on Wednesday. A bolt-action rifle was recovered near the shooting, and a screwdriver was found on the roof from where the fatal shot was fired.

"I can report today that the DNA hits from the towel that was wrapped around the firearm and the DNA on the screwdriver are positively processed for the suspect in custody," Kash Patel told Fox and Friends.

A formal charge is expected this week. A motive has yet to be determined.

The FBI director who has been facing scrutiny over his handling of the case, also referenced a note that was discovered at the suspects home, which vowed "take out" Kirk.

It's "basically saying... 'I have the opportunity to take out Charlie Kirk', and I'm going to take it that note was written before the shooting," said Patel.

He added, "even though it has been destroyed, we have found forensic evidence of the note".

According to a Utah County Sheriff inmate booking sheet obtained by the BBC, Robinson is accused of aggravated murder, obstruction of justice, and felony discharge of a firearm.

The breakthrough comes after the governor of Utah, Spencer Cox, said on Sunday that Robinson - who had been persuaded to surrender by his father - had been refusing to co-operate with investigators and had not confessed to carrying out the shooting.

Cox added that Robinson's roommate and partner, who is believed to be transgender had been helping with the investigation. 

Vice President JD Vance has announced he will host Monday's episode of Kirk's podcast in a tribute to his friend and long-time Trump ally.

Kirk grew to national prominence as a polarising figure in the US after helping found Turning Point USA, a right-wing youth political group, and used his audiences online to build support for often controversial talking points.

The father-of-two had been participating in the American Comeback Tour, visiting several college campuses across the US to debate college students when he was shot.