Few officials expect Mr. Pompeo’s arrival at the State Department to derail the meeting itself, as long as the president and Mr. Kim remain committed to it. But Mr. Tillerson’s departure deprives the White House of the person most experienced in efforts to reach out to North Korea. As the C.I.A. director, Mr. Pompeo has focused more on the threats posed by Pyongyang.

Mr. Pompeo will not be able to establish contact with the South Korean foreign minister, let alone his North Korean counterpart, until the Senate approves his nomination — a process that officials on Capitol Hill said could take several weeks. The White House has not yet even completed the paperwork to begin that process, the officials said.

Adding to the confusion is the lack of official confirmation of a meeting from North Korea. Mr. Kim’s offer was relayed to Mr. Trump by two envoys from South Korea who had recently visited him in Pyongyang. But an American official said Wednesday that the United States and North Korea had still not conferred directly about the meeting through the various diplomatic channels they use.