Kim promised he "will visit Seoul in the near future", and Moon commented Kim would be the first North Korean leader to visit the South.
North Korean leader Kim Jong Un will make a historic visit to Seoul "in the near future", he said Wednesday after a summit with the South's Moon Jae-in in Pyongyang.
After the two leaders signed, military top brass from two Koreas, South Korean defense minister Song Young-moo and his North Korean counterpart No Kwang-chol, also signed the agreement and exchanged the documents.
"While Moon has expressed his desire to agree on a concrete plan on denuclearisation, we believe that the two nations still differ on this concept", said Ms Anwita Basu, an analyst at the Economist Intelligence Unit.
"Kim Jong Un has agreed to allow Nuclear inspections, subject to final negotiations, and to permanently dismantle a test site and launch pad in the presence of global experts".
The United States is pressing countries to strictly observe global sanctions, which will likely be a key theme when Secretary of State Mike Pompeo hosts a Security Council meeting on North Korea on September 27 on the sidelines of the annual U.N. General Assembly.
Pyongyang says it has destroyed its main nuclear and missile engine test site, and has halted atomic and ballistic missile tests, but USA officials and analysts believe it is continuing to work on its weapons plans clandestinely.
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"There is not only going to be a smooth road ahead, there will be challenges and trials, but the more we overcome them the stronger we will become", Kim said.
Earlier this month, Kim's representatives suggested that North Korea would only take action on denuclearization if there was demonstrable "simultaneous" action on the part of the U.S.to show a step down in hostility.
U.S. President Donald Trump welcomed developments on Wednesday at an inter-Korean summit in the North Korean capital of Pyongyang as "very exciting".
At the start of their meeting Tuesday, Kim thanked Moon for brokering the June summit with Trump.
Moon - who went North looking to bring fresh momentum to the stalled effort to eliminate Pyongyang's nuclear weapons - said the trip could happen this year unless there were "special circumstances". The two leaders also announced plans to bid for a joint hosting of the Olympics, oddly enough.
Afterward, Moon will attend a performance of the "Mass Games" - North Korea's spectacular, all-dancing propaganda display.
It stands opposite Mansu hill, where giant statues of Kim's predecessors - his grandfather Kim Il Sung and father Kim Jong Il - look out over the city. "Because of that, the regional political situation has been stabilized and more progress on North Korea-U.S. ties is expected", Kim said, according to South Korean media pool reports and Moon's office.