That appeared to be a subtle but contentious shift in South Korea’s role in the diplomacy around the North’s nuclear weapons. The South and the United States have both said that their relations with the North will develop at roughly the same pace.

But Secretary of State Mike Pompeo has said there will be no sanctions relief on North Korea until denuclearization is complete. American officials also have said the signing of a peace treaty with North Korea to replace the armistice that halted the 1950-53 Korean War — a basic demand of Mr. Kim’s — will not happen before the North denuclearizes.

When Mr. Kim met with President Trump in Singapore two months ago, the leaders adopted a broad, vague agreement on improving bilateral relations, building what they called a peace regime on the Korean Peninsula and denuclearizing it.

But talks between Washington and Pyongyang are deadlocked over differences about how denuclearization should proceed. Meanwhile, the Koreas have been laying the groundwork for improving their relationship on multiple fronts.

Next week, North and South Korea plan to hold another of the periodic reunions of families that were separated during the Korean War of 1950-53. Next month, Mr. Moon is expected to visit North Korea for his third summit meeting with Mr.Kim.

Mr. Moon has bet his political fortunes on resolving the standoff over the North’s nuclear weapons. In his first two meetings with Mr. Kim in April and in May, he came away with an agreement to ease military tensions on the border and boost economic cooperation. Both sides have since conducted field studies on linking their rail networks.