The White House clarified that Mr. Trump would only consider a meeting if the North Korean leader met a series of conditions, starting with a sharp curtailment of his provocative behavior. North Korea carried out its most recent ballistic missile test, which failed, only last week.

“We want to hold out the possibility that if North Korea were ever serious about completely dismantling its nuclear capability and taking away the threat that they pose both to the region and to us,” the press secretary, Sean Spicer, said, “there is always going to be a possibility of that occurring.” But he added, “That possibility is not there at this time.”

For now, the Trump administration is pursuing a more traditional strategy of tightening economic pressure on the North — mainly through its neighbor, China — and backing that up with threat of military action. Mr. Trump said last week that while he wanted to solve the crisis with North Korea through diplomacy, a “major, major conflict” was possible.

Some experts said Mr. Trump’s openness to diplomacy reflected the influence of China, which has long urged the United States to speak directly to North Korea. Since Mr. Trump met last month in Florida with President Xi Jinping of China, he has praised Mr. Xi for what he insisted was China’s willingness to use its leverage over the North to curb its behavior.

“The Chinese have told Trump, ‘You’ve got to talk to these people,’” said Joel S. Wit, an expert on North Korea at Johns Hopkins University, who was involved in diplomacy during the Clinton administration that led to a nuclear agreement with North Korea in 1994.

“They’re trying to create the right circumstances for talks,” Mr. Wit said, “ramping up the pressure on the Chinese, ramping up the pressure on the North Koreans, and then opening up an escape route.”