Authorities have identified the suspect as Tyler Robinson, said the official, who spoke on the condition of anonymity because they were not authorized to discuss the ongoing investigation.
President Donald Trump said Friday "with a high degree of certainty" that the suspect in Kirk's killing has been caught.
Kirk was shot as he spoke to a crowd gathered in a courtyard at Utah Valley University in Orem. More than 7,000 leads and tips had poured in as authorities responded to the latest act of political violence to convulse the United States.
A Mauser .30-caliber, bolt-action rifle was 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 assassination offers the latest example of how ordinary security measures can be defeated in an era of escalating political violence, when anyone associated with the political process is a potential target. Security experts interviewed by AP questioned whether the event was sufficiently staffed but also acknowledged the limitations of both campus police forces and outdoor venues.