“The president’s language, which aides say he had used in private, escalated the long-running dispute with North Korea to a new level and left members of the Trump administration scrambling on Wednesday to explain what he meant.

But the process, or lack of one, that led to the ad-libbed comments embodied Mr. Trump’s overall approach to foreign policy, an improvisational style that often leaves his national security team in the dark about what he is going to say or do, according to several people with direct knowledge of how the episode unfolded.

The president was in a confrontational mood on Tuesday afternoon after The Washington Post reported that Pyongyang had developed nuclear warheads small enough to be placed on ballistic missiles. His team assumed that he would be asked about North Korea during a scheduled media appearance tied to a meeting the president was planning to hold at his golf club in Bedminster, N.J., about the opioid epidemic.

But during a conference call beforehand that focused on North Korea, Mr. Trump did not offer a preview of what he planned to say — and aides did not press the president, who resists being told what to say, even on a tinderbox issue that has induced his predecessors to seek the safety of a script.

He told his aides only that he wanted to signal to Mr. Kim, the North Korean leader, that he was not backing down — while turning up the pressure he has tried to place on China to tame its troublesome neighbor and on-and-off ally.

Mr. Trump’s aides braced as he began to speak at the opioid event — his arms folded, jaw set and eyes flitting on what appeared to be a single page of talking points set before him on the conference table where he was sitting. The piece of paper, as it turned out, was a fact sheet on the opioid crisis.