According to a joint statement, issued after the talks between the two leaders, both Asian nations have agreed to hold talks with the US and China to replace the current ceasefire regime with a peace treaty.
The two countries have agreed to stop all hostile acts toward each other and to transform demilitarized zone into a peace zone, the declaration says.
"South and North Korea reaffirmed the Non-Aggression Agreement that precludes the use of force in any form against each other, and agreed to strictly adhere to this Agreement," the document says.
The parties have also agreed to create a maritime peace zone around the Northern Limit Line in the Yellow Sea (West Sea) to prevent clashes and guarantee safety for fishermen.
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The statement says further that the two leaders have agreed to gradually reduce arms in order to build trust and reduce military tensions in the region, adding that the country's generals will hold a meeting in May to resolve a number of military issues.
"The two sides agreed to hold frequent meetings between military authorities, including the Defense Ministers Meeting, in order to immediately discuss and solve military issues that arise between them. In this regard, the two sides agreed to first convene military talks at the rank of general in May," the document said.
The two Koreas have expressed their wish to improve relations, striving for prosperity and peaceful reunification.
"South and North Korea will reconnect the blood relations of the people and bring forward the future of co-prosperity and unification led by Koreans by facilitating comprehensive and groundbreaking advancement in inter-Korean relation," the document says.
The improvement of relations is "the prevalent desire of the whole nation," the parties added.
Kim Jong-un Promises Moon Jae-in to End Missile Tests
The issues of ridding the Korean Peninsula of nuclear weapons, building peace and improving relations between North and South Korea were on the agenda of their summit on Friday morning, Im Jong-seok confirmed to reporters.
"Both leaders at these talks held a sincere dialogue about the denuclearization of the Korean Peninsula, building a lasting peace and directions for the development of relations between the South and the North," the spokesman said.
North Korea’s leader suggested holding regular summits during a meeting with South’s President Moon Jae-in, Im Jong-seok told reporters.
“Let us meet more often. Let us build a better world,” Im Jong-seok quoted Kim as saying at a briefing after the first round of talks ended in the border village of Panmunjom
According to Seoul, Kim told Moon that Pyongyang "won't interrupt your early morning sleep anymore," referring to missile tests.
Kim's promise was then confirmed by a joint statement issued upon the end of the talks that said, the two Koreas would take measures to support international efforts aimed at denuclearization of the Korean Peninsula.
"South and North Korea confirmed the common goal of realizing, through complete denuclearization, a nuclear-free Korean Peninsula. South and North Korea shared the view that the measures being initiated by North Korea are very meaningful and crucial for the denuclearization of the Korean Peninsula and agreed to carry out their respective roles and responsibilities in this regard," the document added.
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Moon, in his turn, offered, among other things, to link the railroads of the two countries and promised to visit the North in autumn.
"President Moon Jae-in agreed to visit Pyongyang this fall," the document says.
The two leaders also exchanged invitations to each other's capital cities, Im Jong-seok said, telling that Moon Jae-In expressed his interest in visiting North Korea's holy mountain Paektu.
The summit is the third such encounter since the end of the 1950-1953 Korean War. It is being held on the southern side of the demilitarized zone but President Moon briefly stepped over onto the northern soil when the two met on Friday morning.