SpaceX's Crew Dragon astronaut capsule will be ready for its first manned test flight into orbit in the first quarter of next year, provided that "everything goes according to plan" in upcoming tests, NASA chief Jim Bridenstine said on Thursday.

On a visit to the SpaceX headquarters, Bridenstine praised Elon Musk's company for its "fail fast, then fix" approach to spacecraft design after a personal tour and briefing at the sprawling manufacturing plant - a display of unity amid a rare public spat between the two key space figures. 

But he also emphasized NASA's concern for astronaut safety, saying the timeline could slip. 

"We are not going to take any undue risk," Bridenstine said, standing beside Musk outside a clean room that contained a Crew Dragon capsule. 

The National Aeronautics and Space Administration is paying commercial launch contractors SpaceX and Boeing Co 6.8 billion U.S. dollars to build rocket-and-capsule systems to return astronauts to the International Space Station from U.S. soil for the first time since America's space shuttle program ended in 2011. 

Bridenstine's visit to SpaceX headquarters in the Los Angeles suburb of Hawthorne comes as SpaceX works to overcome key technical challenges on the Crew Dragon. SpaceX has so far never flown humans into orbit, only cargo.

Musk and Bridenstine said they were working together through concerns over re-entry parachutes and other technical challenges, some of which were first publicly detailed by Reuters.

"It's a pretty arduous engineering job to get the parachutes right," Musk said, declaring that Crew Dragon's parachutes will have "twice the safety factor" than those used in the Apollo era.

"Testing will be complete and hardware at the Cape (Canaveral) by the end of December," he added.

While Musk and Bridenstine provided few concrete details on their joint investigation into an explosion during a capsule ground test in April, Musk said incidents were inevitable during complex development processes and rigorous testing.

The visit follows a dispute over the last two weeks between Musk and the NASA chief, who bristled at Musk on Twitter for celebrating an unrelated milestone achieved on SpaceX's deep-space Starship rocket while completion of the Crew Dragon project remained delayed.

Musk quickly shot back during a series of interviews, at one point citing a rival NASA moon rocket dubbed the Space Launch System that is years behind schedule and billions of dollars over budget. He also told CNN "most of the work" left to complete on Crew Dragon was related to "a long series of safety reviews" by NASA.

Both the Boeing and SpaceX capsules have been beset by delays and testing mishaps that have prevented either company from achieving goals for manned orbital missions in 2019.

（Cover: File photo of a SpaceX Falcon 9 rocket with the company's Crew Dragon spacecraft on board. /Reuters Photo）