US President Donald Trump lashed out at the "radical left" after the apparent assassination of his right-wing ally Charlie Kirk, promising a crackdown after a killing that has sparked fears of worsening political violence in the United States.

Kirk, a powerful voice in conservative politics at just 31 years old, had been dead only a few hours when a somber-looking Trump sat behind his desk in the Oval Office to deliver an ominous message.

"This is a dark moment for America," he said on video posted to his Truth Social website, hailing Kirk as a "martyr for truth".

"For years those on the radical left have compared wonderful Americans like Charlie to Nazis and the world's worst mass murderers and criminals.

"This kind of rhetoric is directly responsible for the terrorism that we're seeing in our country today.

"My administration will find each and every one of those who contributed to this atrocity, and to other political violence, including the organizations that fund it and support it."

Investigators said they believe the bullet that killed him had come from a campus rooftop, fired by someone dressed in black, in what appeared to be a targeted killing.

There was confusion over the manhunt, with FBI director Kash Patel initially tweeting that the "subject" had been detained, before walking that back an hour later.

"The subject in custody has been released after an interrogation by law enforcement. Our investigation continues," he wrote on X.

Illustrating the huge importance of Kirk in Trump's orbit, the 79-year-old Republican ordered flags on government buildings – including the White House – to be lowered to half-staff until Sunday.

"No one understood or had the Heart of the Youth in the United States of America better than Charlie. He was loved and admired by ALL, especially me, and now, he is no longer with us," Trump wrote.

News of the shooting provoked horror across the political spectrum.

"Eternal rest grant unto him, O Lord," Vice President JD Vance posted on social media.

Right wing media personality Tomi Lahren called Kirk "visionary."

Figures on the left also condemned the attack and urged calm.

"There is no place in our country for this kind of violence. It must end now," former president Joe Biden wrote on X.

California governor Gavin Newsom – a frequent foil for right-wing figures like Kirk – called the attack "disgusting, vile, and reprehensible".

Former congresswoman Gabrielle Giffords – a Democrat who herself survived an assassination attempt – said she was "horrified" by the attack.

"Democratic societies will always have political disagreements, but we must never allow America to become a country that confronts those disagreements with violence," Giffords said.

Kirk's killing came three months after a Minnesota man shot dead a Democratic lawmaker and her husband in their home. (AFP)