Investigators obtained clues, including a palm print, a shoe impression and a high-powered hunting rifle found in a wooded area along the path the shooter fled.
But they have yet to name a suspect or cite a motive in the killing, the latest act of political violence to horrify the United States across the ideological spectrum.
Photos have been released of a 'person of interest', who was wearing a hat, sunglasses and a long-sleeve black shirt, with a backpack.
As well a $100,000 reward for information leading to an arrest suggests that law enforcement thought tips from the public may help to crack the case.
Two people who were taken into custody shortly after the shooting at Utah Valley University were later released without charge. After their identities became known, they were subjected to threats.
President Donald Trump has urged mourning Americans not to respond with further acts of violence.
One lead in the investigation was a 30-calibre, bolt-action rifle found in a towel in the woods. A spent cartridge was recovered from the chamber, and three other rounds were loaded in the magazine, according to information circulated among law enforcement and described to The Associated Press. The weapon and ammunition - said to be inscribed with messages - were being analysed by law enforcement at a federal lab.
The attack, carried out in a broad daylight as Kirk spoke from a university courtyard, was captured on grisly videos that spread on social media.
The videos show Kirk, a close ally of Trump, speaking into a handheld microphone when a shot rings out. Kirk can be seen reaching up with his right hand as blood gushes from the left side of his neck. Stunned spectators gasp and scream before people start running away.
The shooter, who investigators believe blended into the campus crowd because of a "college-age" appearance, fired a single shot from the rooftop where they were perched before jumping off.
Vice President JD Vance and his wife, Usha, accompanied Kirk's widow Erika, as his body was flown from Utah to his home state of Arizona on board Air Force Two.
Supporters gathered at the airport in Phoenix, waving flags, while a voice on the Air Traffic Control frequency said "Welcome home, Charlie. You didn't deserve it. May God bless your family,"
Vance posted a remembrance on X chronicling their friendship, dating back to 2017, through Vance's Senate run and the 2024 election.
Trump said he would be attending Kirk's funeral, and would award the influential commentator the Presidential Medal of Freedom, the highest civilian honour in the US.
Kirk was a conservative provocateur who became a powerful political force among young Republicans and was a fixture on college campuses, where he invited sometimes-vehement debate on social issues.
One such provocative exchange played out immediately before the shooting, as he was taking questions from an audience member about gun violence when the shot was heard.
The shooting continued to draw bipartisan condemnation as Democratic officials joined Trump and other Republican allies of Kirk in decrying the attack, which unfolded during a spike of political violence that has touched a range of ideologies and representatives of both major political parties.
"The murder of Charlie Kirk breaks my heart. My deepest sympathies are with his wife, two young children, and friends," said Gabrielle Giffords, the former Democratic congresswoman who was wounded in a 2011 shooting in her Arizona district.
with DPA and AP
