Kash Patel, the F.B.I. director, said that the agency's investigation was continuing, reversing his earlier announcement that someone had been apprehended.
President Trump asked for updates and met with advisers in the Oval Office before recording a four-minute video in which he blamed rhetoric from the "radical left" for the killing.
The founder of Turning Point USA played a central role in organizing young voters and giving shape to the pro-Trump agenda. He was fatally shot during a speaking event in Utah.