SEOUL, South Korea — President Moon Jae-in of South Korea said on Wednesday that he and President Trump could sit down for a three-way summit meeting with Kim Jong-un if their individual meetings with the North Korean leader on denuclearizing his country proceed well in the coming weeks.

Mr. Moon and Mr. Kim are planning an inter-Korean summit in late April at Peace House, a South Korean conference hall inside Panmunjom, the so-called truce village that straddles the Demilitarized Zone, or DMZ, separating the two Koreas.

That meeting is expected to be followed by a planned Trump-Kim summit meeting by May. If that meeting takes place, Mr. Trump will be the first-ever sitting American president to meet a North Korean leader; Washington and Pyongyang are still technically at war because the 1950-53 Korean War was halted with a truce, rather than a peace treaty.

While presiding over a meeting Wednesday of government officials preparing for the inter-Korean summit, Mr. Moon attached great significance to the venue for his coming meeting with Mr. Kim.