A visit by the NASA administrator to a rocket factory is usually a predictable show-and-tell of the latest gadgets destined for outer space.

But there may have been some tension below the surface on Thursday when the current administrator, Jim Bridenstine, stopped by the headquarters of SpaceX, the private rocket company of the billionaire Elon Musk, in Hawthorne, Calif. SpaceX is a major contractor for NASA.

Mr. Bridenstine and Mr. Musk had been exchanging nettlesome messages for the past two weeks. Thursday’s visit might have been as much about smoothing over ruffled feelings as viewing space hardware.

Taking questions from reporters, both men were complimentary toward each other and said they shared the same goals: to launch NASA astronauts to the International Space Station on SpaceX’s Crew Dragon capsule as soon as possible, but not before the spacecraft had passed all of the needed tests.