The press secretary, Sarah Huckabee Sanders, was hardly more forthcoming.

“If they want to meet, we’ll be ready,” she told reporters on Wednesday, “and if they don’t, that’s O.K., too.” She said the White House “fully expected” North Korea to take this tack — an assertion belied by the scrambling of officials when the first reports came in from Pyongyang on Tuesday evening.

Other officials, however, insisted that they were taking North Korea’s warnings in stride, noting that Mr. Kim, not Mr. Trump, had sought the meeting. They said they expected the North to maneuver for tactical advantage until the two leaders met on June 12.

People close to the White House said the scattershot nature of the messages on North Korea 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 the payments made by his personal lawyer, Michael D. Cohen, to a pornographic film actress.

Some suggested that Mr. Trump needed to rein in Mr. Bolton — a point the North Korean official, Mr. Kim, appeared to be making in his statement. He rejected Mr. Bolton’s reference to Libya as a template for North Korea, saying that the “world knows too well that our country is neither Libya nor Iraq, which have met miserable fates.”

If Pyongyang’s statements caught Washington and Seoul off guard, they reflected a well-established North Korean position: that it is only willing to negotiate with the United States as a fellow nuclear power.

By referring to itself as a “nuclear weapon state,” North Korea was not only distinguishing itself from Libya or Iraq, it was also potentially signaling that the North is seeking an arms control agreement, not disarmament. Under such an arrangement, analysts said, North Korea would be treated like the Soviet Union and later Russia, which were asked to limit, rather than eliminate, their arsenals.