Chung Eui-yong had come to the White House bearing an invitation. But he opened with flattery, which diplomats have discovered is a key to approaching the volatile American leader. “We could come this far thanks to a great degree to President Trump,” Mr. Chung said. “We highly appreciate this fact.”

Then he got to the point: The United States, South Korea and their allies should not repeat their “past mistakes,” but South Korea believed that North Korea’s mercurial leader, Kim Jong-un, was “frank and sincere” when he said he wanted to talk with the Americans about giving up his nuclear program. Mr. Kim, he added, had told the South Koreans that if Mr. Trump would join him in an unprecedented summit meeting, the two could produce a historic breakthrough.

Mr. Trump accepted on the spot, stunning not only Mr. Chung and the other high-level South Koreans who were with him, but also the phalanx of American officials who were gathered in the Oval Office.

Those officials thought the president would take more time to discuss such a decision with them first. Defense Secretary Jim Mattis and Lt. Gen. H.R. McMaster, the president’s national security adviser, both expressed caution. If you go ahead with this, they told Mr. Trump, there will be risks and downsides.