And while in New York, President Moon gave an interview to cable news giant Fox News, in which he said both South and North Korea and the United States have the same idea when it comes to ending the Korean War.
And as for the North's denuclearization, he said this latest push is different from those of the past.
Shin Se-min reports.
Speaking to Fox News, President Moon Jae-in discussed the outcomes of diplomacy with North Korea.
The President said the regime will in fact give up its nuclear weapons because the promise to do so comes from the very top of the regime's chain of command.
He said that although many are skeptical about whether North Korea really will follow through,... the latest agreements, including the one between leader Kim Jong-un and U.S. President Donald Trump,... are different from those of the past.

President Moon also spoke for Kim, whose promises, he said -- to allow outside inspections of key nuclear test sites and to dismantle facilities -- are in sync with the U.S. policy of Complete, Verifiable and Irreversible Denuclearization, or CVID.
The President also alluded to what that the "corresponding measures" Pyeongyang wants from Washington might be.
He said they could be a formal declaration ending the Korean War, or humanitiarian aid of some sort, maybe non-political exchanges like cultural networking -- or even setting up a U.S. liaison office in Pyeongyang.

And touching upon South Korea's ironclad alliance with Washington,... the President added that officially ending the Korean War would not hamper the allies' strong connection.

And speaking with a group of some 200 opinion leaders with close links to Korea issues, the President also shared his take on diplomacy with the North.
He explained Kim Jong-un's point of view as expressed in their latest meeting in Pyeongyang.

"He (Chairman Kim) said, what would the North gain from deceiving or wasting time? If they did that, he said, the U.S. would come back with strong retaliation and how would the North deal with that? Now is the time."

"The president's message in New York is clear,... the major players in the region,... the two Koreas and the United States,... have one firm goal in mind. Opening up a new era of everlasting peace and prosperity on the Korean Peninsula as a team,... by seeing through the denuclearization of North Korea and ending the decades-long Korean War.
Shin Se-min, Arirang News, New York."