The Marine Corps acting commandant, Eric Smith, on Monday issued a two-day stand-down to take place at some point this week for all aviation units both inside and outside of the United States, a spokesman told ABC News.

The move was made in the wake of a "mishap" with an F-35 fighter jet in South Carolina on Sunday outside Joint Base Charleston, where it had taken off from, according to military authorities.

That craft has not yet been located, though the military continues to search.

No Marine Corps units are allowed to fly until they have a two-day discussion about safety measures and procedures, the commandant said in a service-wide email on Monday. While Smith said he has full confidence in the aviation units, he said he felt this was the "right and prudent" thing to do given both this incident and another recent incident in Australia.

A Marine Corps spokesperson said in a statement on Sunday that the missing F-35's pilot "safely ejected from the aircraft. We are currently still gathering more information and assessing the situation. The mishap will be under investigation."

A spokesman at Joint Base Charleston said the jet was left on autopilot when the pilot ejected.

White House spokesman John Kirby said later Sunday on MSNBC that the U.S. still didn't know where the F-35 is, and he said he didn't know more about the reported mishap.

"We're staying in touch with the Pentagon as much as we can," he said. "Right now, we just don't know where that aircraft is. We're glad that pilot was able to eject safely [and we're making] sure he gets the medical care he needs."

"First thing, we need to literally try to find the aircraft. Then they'll have a chance to talk to the aviator when they get a chance," he said.

ABC News' Ben Gittleson, Nathan Luna, Noah Minnie and Martha Raddatz contributed to this report.