Mr. Trump demonstrated his deference to North Korea in an interview taped before he left Singapore and aired on Fox News on Wednesday night. When Mr. Kim’s record of ordering the deaths of members of his own family and presiding over one of the most repressive states in the world was mentioned, Mr. Trump said, “Yeah but so have a lot of other people, done some really bad things. I mean, I could go through a lot of nations where a lot of bad things were done.”

He also expressed willingness to withdraw American troops stationed in South Korea since the end of the Korean War 65 years ago, a longtime goal of the North’s. While Mr. Trump said it was not currently on the table in their negotiations, he wanted to do it for his own reasons. “I would love to get the military out as soon as we can because it costs a lot of money,” he said.

If the talks in Singapore provided Mr. Trump an opportunity to show statesmanship on a grand scale, they did no less for Mr. Kim, whose country has long sought such a meeting with an American president. The state-run newspaper Rodong Sinmun plastered the pages of its Wednesday edition with color photographs of Mr. Kim and Mr. Trump talking, walking and smiling, apparently as equals, with the flags of the two countries arranged side by side as a backdrop.

“The critical question is what comes next?” said Kelsey Davenport, the nonproliferation policy director at the Washington-based Arms Control Association. “The true test of success is whether the follow-on negotiations can close the gap between the United States and North Korea on the definition of denuclearization and lay out specific, verifiable steps that Pyongyang will take to reduce the threat posed by its nuclear weapons.”

Secretary of State Mike Pompeo, who traveled to Seoul to brief South Korean officials, said the next step in negotiations had not been decided, but added that he expected to “begin the engagement” with North Korea within the next week.

Speaking with reporters, he said that the Trump administration hoped to complete the “major disarmament” of North Korea within the next 2½ years without defining what that would entail. Some nuclear experts have said completely unwinding North Korea’s nuclear program could take 10 to 15 years, although some foreign policy analysts said the two sides could accomplish enough by the end of Mr. Trump’s term in office to demonstrate a serious effort.