There had been local media speculations that the two Koreas already agreed upon the date and venue for the third Moon-Kim summit as the two sides had working-level contacts before the high-level dialogue.
According to the reports, a 34-year-old man surnamed Suh drove an SUV through the checkpoint on the South Korean side of the Unification Bridge in Paju, Gyeonggi Province, which leads to the Demilitarized Zone separating the two Koreas, without undergoing proper inspection.
The Koreas said in a statement that they reviewed ways to set up agreements made at the past summits during almost two hours of talks Monday.
Moon and Kim agreed during their first summit to push for a declaration of an end to the Korean War together with the United States this year, but Washington has said it would only be possible after the North abandons its nuclear program.
Cho, the chief of the South Korean delegation, said the two sides also "talked a lot" about worldwide sanctions meant to punish the North for its development of nuclear weapons, but he didn't elaborate.
The North has been heavily sanctioned over its pursuit of nuclear weapons and ballistic missiles but Mr Kim and US President Donald Trump agreed at their landmark summit in Singapore in June to work towards the denuclearisation of the Korean peninsula.
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The countries' chiefs of inter-Korean affairs met for almost two hours at the border village of Panmunjom before making the announcement.
Moon is apparently hoping to use the meeting to encourage Kim to proceed with denuclearization as the US-North Korea negotiations on the issue have stalled.
Officials from the two sides are expected to discuss ongoing economic projects and settle on some details for the inter-Korean summit they agreed to hold this fall.
The South Korean Unification Ministry announced the upcoming meeting after a round of high-level talks between officials from Pyongyang and Seoul at the DMZ Monday.
"Whether that is true is in doubt but they are trying to indirectly pressure the U.S., especially on sanctions, by showing an improvement in North-South ties and that peace has been established between them".
Experts say there has been slow progress on those efforts since the Singapore summit.