Mr. Kim countered with a more incremental offer — that North Korea would dismantle its aging Yongbyon nuclear complex in return for lifting the most onerous sanctions against the North. Mr. Trump’s aides, notably the national security adviser, John R. Bolton, warned him against taking such a deal.
The timing of the meeting, analysts said, may have added to Mr. Trump’s caution. As he and Mr. Kim were facing off in Hanoi, lawmakers in Washington began their televised interrogation of Mr. Trump’s former lawyer, Michael D. Cohen — a split-screen drama that could have fed perceptions, had the president accepted a deal, that he was merely looking for a way to change the subject.
Six weeks later, after the disclosure that the special counsel, Robert S. Mueller III, did not find evidence of a conspiracy between the Trump campaign and Russia during the 2016 election, the legal cloud over Mr. Trump has lifted a bit. That could make the president more willing to take a risk at the bargaining table.
Analysts said they could envision a way to square Mr. Kim’s incremental approach with Mr. Trump’s big-bang ambitions. North Korea, they said, could offer to dismantle Yongbyon, along with a freeze on its program, in return for limited sanctions relief. The two sides could then agree on a road map that would lead to North Korea’s complete denuclearization and the full lifting of sanctions.
“If they could get an agreement on the end goal, that would be the big deal in principle,” said Victor D. Cha, a professor at Georgetown University who negotiated with North Korea during the George W. Bush administration. “That’s not a bad place for the U.S. to be, in terms of leverage.”
Behind closed doors, analysts said Mr. Moon probably pushed Mr. Trump to show more flexibility on sanctions. But publicly, he took pains to stay on the same page as the president, insisting there was “no daylight” between South Korea and the United States on the goal of ridding North Korea of its arsenal.
For Mr. Moon, however, cajoling Mr. Kim back to the table could be harder than it is with Mr. Trump. The psychological impact of Mr. Kim being rebuffed in Hanoi cannot be overestimated, given that he is a 35-year-old leader who has ruthlessly put down any challenges to his rule, experts said.