But while containing several tantalizing offers, their joint statement appeared to fall short of the major steps many in Washington have been looking for - such as a commitment by Kim to provide a list of North Korea's nuclear facilities, a solid step-by-step timeline for closing them down, or an agreement to allow worldwide inspectors to assess progress or discover violations.
"The North agreed to permanently close the Tongchang-ri missile engine test site and missile launch facility in the presence of experts from relevant nations", Moon told reporters. The Dongchang-ri complex has been a key test center for the North's intercontinental ballistic missile program. The two sides have exchanged fire along the border 96 times since the armistice was signed, halting the Korean War in 1953.
"The South and North agreed to actively participate jointly in global competitions including the 2020 Summer Olympics and to cooperate in bidding for the South-North joint hosting of the 2032 Summer Olympics", the statement said. The leaders met on the Korean border in April and May. The countries' defense chiefs have meanwhile signed a separate military pact.
To transform the DMZ into a "peace zone", they will each pull out 11 guard posts on a trial basis by the end of this year and halt drills targeting each other near the MDL starting November 1.
North Korea's leader Kim Jong Un offered on Wednesday to permanently dismantle the country's main nuclear site, but only if the United States makes concessions first. The president also called the possible joint-Korea bid for 2032 "Very exciting!".
A joint statement also says the two Koreas have agreed to seek to obtain the rights to co-host the 2032 Summer Olympics.
The proposal, presented during the meeting between South Korean President Moon Jae-in and North Korean leader Kim Jong-un in Pyongyang, was first put forward by the South Korean Sports Minister Do Jong-hwan during a visit to Tokyo on September 12 and could mean a joint hosting of events by Seoul and Pyongyang, reports Efe.
Kim has previously committed to working toward denuclearization, in joint statements with both Moon and Trump. The news conference was broadcast live.
"The inter-Korean summit will be a litmus test for another meeting Kim has recently proposed to U.S. President Donald Trump, giving clues to whether Kim is serious about denuclearisation, a commitment he made at their first encounter in June", writes Yahoo News.
How you see the third summit this year between Moon and Kim - and there could be another in the works, with Kim promising to come to Seoul soon - may depend on where you're sitting, both geographically and politically.
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Later on Wednesday, Moon's delegation is scheduled to tour the Mansudae Art Studio, the North's largest producer of art and propaganda, which was sanctioned by the United Nations previous year.
Kim's late father, Kim Jong Il, had promised reciprocal visits when South Korean leaders visited him in Pyongyang in 2000 and 2007. However, it is conditional upon the United States taking undefined "corresponding measures". At the same time, the North is continuing to expand its nuclear arsenal. As Inter-Korean exchanges pick up speed, a key goal for Moon will be to sell the rapid rapprochement to his own people, with many remaining sceptical of pandering to a brutal dictator.
Demilitarization of the Joint Security Area (JSA) in the truce village of Panmunjom will also go ahead, the MND said, adding that a trilateral consultation body between the two Koreas and the United Nations Command (UNC) will be established.
Then, Trump is expected to decide whether he will meet with Kim again.
He also expressed hope to keep up the momentum of talks to bring about another summit between North Korea and the U.S.
On Thursday, the last day of his three-day visit, Moon plans to visit Mount Baektu in North Korea with Kim before returning home.
When Moon stepped off his plane, a smiling Kim was waiting on the tarmac with a military honor guard and a large crowd of citizens mobilized for his arrival. Standing side by side after their second day of talks, they declared they had made a major step toward an "era of peace and prosperity" on the Korean Peninsula.
Kim and Moon share a toast during a welcome banquet in Pyongyang on Tuesday.
"Chairman Kim has clearly shown a way to denuclearisation on the Korean peninsula today". The facilities were a key test center for its intercontinental ballistic missiles created to reach the United States.
Showing Moon and his wife, Kim Jung-sook, to their suite in the state guesthouse, Kim sounded apologetic about the state of the North's economy, as he has before with Moon.
"I don't think President Moon got everything he was seeking from these interactions, but Kim Jong Un gave Moon some tangible things for which he can take credit", said Michael Madden, an analyst at the Stimson Centre's 38 North think tank in Washington.