Mr. Pompeo, by contrast, put the emphasis on the American investment that would flow into North Korea if it agreed to relinquish its nuclear arsenal. He, too, said that the North would have to agree to “complete, verifiable, irreversible denuclearization,” the technical shorthand used by the administration to describe its bargaining position with Pyongyang.

The president has shifted between a hard-line and more conciliatory tone in his statements about the North, although in recent days he has expressed excitement about a potential breakthrough with Mr. Kim. He has not yet responded to the warning Wednesday issued by the North’s first vice foreign minister, Kim Kye-gwan, which took direct aim at Mr. Bolton.

People close to the White House said the uncoordinated nature of the statements reflected the newness of the president’s national security team, but also the fact that Mr. Trump was distracted by the swirl of legal issues around him, from the Russia investigation to payments his personal lawyer, Michael D. Cohen, made to a pornographic film actress.

Some officials suggested that Mr. Trump needed to rein in Mr. Bolton, though they expressed few qualms about the White House’s broader strategy. Officials noted that the United States had not made any concessions to Mr. Kim, beyond agreeing to the meeting itself. Mr. Kim has agreed to stop nuclear and missile tests and to blow up an underground nuclear site in the presence of foreign journalists.

While the daylight between Mr. Bolton and Mr. Pompeo gives the North Koreans the opportunity to drive a wedge between members of the president’s national security team, officials said that was a more manageable problem than when Mr. Trump publicly undercut Mr. Pompeo’s predecessor as secretary of state, Rex W. Tillerson, over how to deal with North Korea.

Assessing the North’s recent statements, Koh Yu-hwan, a professor of North Korean studies at Dongguk University in Seoul, said North Korea had begun to fear looking weak by taking unilateral steps, like its moratorium on missile tests. He noted that the United States, rather than offering concessions of its own, has vowed to keep up its maximum pressure on the North if it fails to quickly denuclearize.