But a senior United States official involved in North Korean policy said there was no way to know if North Korea would agree to this. In the past, he said, its negotiators have insisted that only Mr. Kim himself could define what dismantling Yongbyon meant.

To make any deal work, the North would have to agree to include many facilities around the country, among them a covert site called Kangson, which is outside Yongbyon and is where American and South Korean intelligence agencies believe the country is still producing uranium fuel.

A president embarking on a re-election campaign — and who complained repeatedly on Sunday that he receives no credit from the media for de-escalating tensions with North Korea and for the freeze on underground nuclear tests and test-launches of intercontinental ballistic missiles — would most likely cast this as a victory, as another restraint on Mr. Kim. It would help Mr. Trump argue that he is making progress, albeit slowly, on one of the world’s most intractable crises.

And it would be progress after three face-to-face meetings — first in Singapore a little more than a year ago, then in Hanoi, then in an hourlong discussion at the DMZ on Sunday — that have produced warm exchanges but no shared definitions of what it meant to denuclearize the Korean Peninsula. A year after that first meeting, the North has yet to turn over an inventory of what it possesses, claiming that would give the United States a map of military targets.

On Sunday evening, the State Department’s envoy to North Korea, Stephen E. Biegun, said that this account of the ideas being generated in the administration was “pure speculation” and that his team was “not preparing any new proposal currently.”

“What is accurate is not new, and what is new is not accurate,” he said.

Presumably, Mr. Trump’s freeze would have to be a permanent one, or he will have gotten less from Mr. Kim than President Barack Obama got from Iran in a deal Mr. Trump dismissed as “disastrous.” And even a successful freeze would constitute a major retreat from the goal of the “rapid denuclearization of North Korea, to be completed by January 2021,” as Mr. Pompeo put it last fall.