Washington has demanded concrete action toward denuclearisation, such as a full disclosure of North Korea's nuclear and missile facilities, before agreeing to key goals of Pyongyang, including an easing of global sanctions and an official end to the Korean War.
There, Kim promised to allow external inspectors into his country to verify that a missile test and launch site had been permanently dismantled, and he pledged to permanently disable an important nuclear site if the United States also takes "corresponding steps".
The question is whether it will be enough for President Donald Trump to pick up where Moon has left off. Trump told reporters Wednesday that the outcome of the summit was "very good news" and that "we're making tremendous progress" with North Korea.
A representative of the State Department did not immediately respond to a request for comment.
The two sides agreed to break the impasse during Kim Jong Un's historic meeting with Trump in Singapore in June.
He also set a January 2021 deadline for North Korea's denuclearization.
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The Korean War ended in 1953 with an armistice rather than a peace deal.
Even if North Korea were to shut down Yongbyon, officials and experts believe it has other secret nuclear facilities.
U.S. officials suggested Kim was trying to ease the economic pressure on him to curb his nuclear programs and to undercut the rationale for United States troops being based in South Korea by improving relations with Seoul.
Moon's spokesman, Yoon Young-chan, announced later in the day that the South Korean President would travel to the U.S. to meet with Trump on September 24.
Moon and Kim have sought to strengthen the North-South relationship at their Pyongyang summit, agreeing that the North Korean leader will visit Seoul "at an early date".
The South Korean leader also said he'll convey to Trump his and Kim's desire to get a declaration ending the Korean War by the end of this year.
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With the main business of the day over, North Korea was expected to hold a huge mass games spectacle in the evening, with Moon as the special guest.
"I propose we move forward toward the big picture of peace in which the past 70-year-long hostility can be eradicated and we can become one again", he said, prompting rapturous applause.
But while Moon's warm reception in the North Korean capital and smiling photo opportunities have already been considered a diplomatic victory, a number of global policy experts are still uncertain as to whether facility shutdowns in Yongbyon will actually cease all nuclear production, with the Times noting that some foreign analysts suspect that Kim has other nuclear programs operating in secret.
The 2 744m peak is considered sacred to all Koreans as the birthplace of Dangun, the legendary founder of the first Korean kingdom.
Plans were laid out for a reciprocal visit by Mr Kim to Seoul - which would make him the first North Korean leader to do so.
The South Korean President said he and Kim would work together to create a "new era", saying the two had agreed "to eliminate the fear of war and danger of armed conflicts on the Korean peninsula".
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After visiting the mountain, Moon is scheduled to return to Seoul, flying directly to Seongnam Air Base from Samjiyon, wrapping up his three-day visit.