SEOUL, South Korea — President Moon Jae-in of South Korea urged the United States on Thursday to declare an end to the Korean War as an incentive for North Korea to denuclearize, a call that could put the Trump administration in a bind as it tries to revive stalled talks with Kim Jong-un, the North’s leader.

Mr. Moon said that during his landmark three-day summit meeting with Mr. Kim this week, the North’s leader had repeatedly expressed willingness to give up his nuclear weapons quickly and to build new relations with Washington.

“He again and again reaffirmed his commitment to denuclearization,” Mr. Moon said at a news conference in Seoul, the South’s capital, after returning from North Korea. “He said he wanted to achieve complete denuclearization as soon as possible and focus on economic development.”

To “expedite denuclearization,” Mr. Moon said, Mr. Kim also hopes to meet Secretary of State Mike Pompeo in Pyongyang, the capital of North Korea, and to hold a second meeting with President Trump as soon as possible. Mr. Trump and Mr. Kim first met in Singapore in June.