When Mr. Trump sent his letter last week to Kim Jong-un canceling — or at least postponing — the summit meeting, one of the likely triggers was a statement from Choe Son Hui, a North Korean vice foreign minister, in which she criticized Vice President Mike Pence for “ignorant and stupid” remarks comparing North Korea and Libya.

But she has been representing the North in talks with an American delegation led by Sung Kim, a veteran diplomat and ambassador to the Philippines. The two sides met on Sunday in Panmunjom, a “truce village” in the Demilitarized Zone that separates the two Koreas.

The diplomats and technical experts are probably working out an agenda for the meeting, and the American side is looking to secure detailed commitments from Kim Jong-un that his regime is willing to abandon its nuclear weapons program.

Analysts said that Ms. Choe and Mr. Kim were likely to work on drafts of a potential declaration that could be issued at the summit meeting, with wording from North Korea about getting rid of its nuclear weapons and a guarantee from the United States that it would not interfere with the North’s regime or demand redress for human rights abuses.

“Ms. Choe is probably asking for nonaggression and even the stopping of joint military drills between the U.S. and South Korea because the North feels threatened by it,” said Chon Hyun-joon, a visiting professor at Woosuk University in Jeongju City. “The North Koreans are very good at getting what they want at the last minute, while it seems Trump is a little more impatient.”

Ms. Choe was an interpreter for the North Koreans during previous nuclear negotiations known as the six-party talks, which started in 2003 and eventually broke down in 2009. She is likely to have previously met Sung Kim at conferences in Europe as well.