Moon has been instrumental in brokering the diplomatic thaw that saw a historic summit between Kim and US President Donald Trump in Singapore in June, where Kim backed denuclearization of the Korean peninsula.
Inter-Korean relations have been significantly improving since Kim Jong Un pledged in his New Year's address on January 1 that he would prepare for his country's participation in the Feb 9-25 Pyeongchang Winter Olympics hosted by the South.
Economic co-operation between North and South is nothing new. There will be no U.S.
Seoul said that could lay the groundwork for a formal declaration on the Korean War, when hostilities ended in an armistice rather than a peace treaty - implying that such an announcement was unlikely during the trip.
Moon and his entourage were welcomed by reporters, members of the North Korean military, a military band, and North Koreans wearing suits, hanboks (traditional clothes), and holding North Korean and unified peninsula flags, as well as flowers. Lindsey Graham, who tweeted he was concerned the visit would undermine efforts by Secretary of State Mike Pompeo and U.N. Ambassador Nikki Haley to impose "maximum pressure" on Pyongyang. But in August, Defense Secretary James Mattis said the US had no future plans to end the joint military drills.
On Sunday, thousands of North Korean troops, followed by artillery and military tanks, paraded through Pyongyang, but the celebration lacked the usual jingoism that has been associated with the isolated regime for decades.
Rarely do the North Korean official media even mention the word denuclearization.
During Tuesday's afternoon briefing to reporters, Yoon said it was unclear how much progress would be made on denuclearization issues and that it would be necessary to wait until after Wednesday's talks before any conclusions, if any, would be announced.
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Agreeing on a timetable is a core task for Moon, as it would induce USA action, said Lee Jung-chul, a professor at Soongsil University in Seoul.
The summit came a day after U.S. U.N. Ambassador Nikki Haley called out Russian Federation and China for consistently skirting U.N. sanctions against North Korea, during an urgent Security Council meeting called by the U.S. The sanctions are aimed at pressuring the regime to abandon its nuclear and missile programs.
During a Cabinet meeting last week, Moon said he needs not only strong global support but also "nonpartisan backing at home" to help make next week's summit produce a major step toward denuclearization.
Currently, all major joint projects between the Koreas are stalled because of US-led sanctions. "Beyond the nuclear issue, the two Koreas have their own vast, multifaceted agenda". During their summit, the two generally agreed to the denuclearization of the Korean Peninsula, but did not set out a concrete plan.
Both China and Russian Federation backed United Nations sanctions against North Korea over its nuclear program, though both countries would benefit from projects like updating and expanding North Korea's railway system, Lee said.
Mr Moon said he wants "to find a middle ground between a United States request for (North Korea's) denuclearisation and the North's request for corresponding measures such as ending hostile relations and security assurances". "They should be free to pursue this as this would be good for building peace".
An undated photo shows a march for peace, prosperity and reunification of Korea in Pyongyang, North Korea.
At a meeting with senior advisers to the summit preparations committee Thursday, Moon said North Korea should scrap its existing nuclear weapons program and nuclear materials, and that there was room for Washington and Pyongyang to end the current deadlock. That's important because China is the North's biggest economic partner and is an important political counterbalance to the United States.