The two also agreed to push towards turning the armistice that ended the Korean War in 1953 into a peace treaty this year. It comes just months after warlike rhetoric from North Korea.
Details of how denuclearisation would be achieved were not made clear and many analysts remain sceptical about the North's apparent enthusiasm for engagement.
Following discussions at the summit on Friday, Mr Kim said that both leaders had agreed to co-ordinate closely to ensure that there was not a repeat of the region's "unfortunate history" in which previous progress had "fizzled out".
"There may be backlash, hardship and frustration," he said, adding: "A victory cannot be achieved without pain."
Other points the leaders agreed on in a joint statement were:
- An end to "hostile activities" between the two nations
- Changing the demilitarised zone (DMZ) that divides the country into a "peace zone" by ceasing propaganda broadcasts
- An arms reduction in the region pending the easing of military tension
- To push for three-way talks involving the US and China
- Organising a reunion of families left divided by the war
- Connecting and modernising railways and roads across the border
- Further joint participation in sporting events, including this year's Asian Games
The leaders were met on Friday by an honour guard in traditional costume on the South Korean side. The pair walked to the Peace House in Panmunjom, a military compound in the DMZ between the two countries.
Mr Kim then invited the South Korean president to step briefly across the demarcation line into North Korea, before the pair stepped back into South Korea - all the while holding hands.
It was an apparently unscripted moment during a highly choreographed sequence of events.
When the first session ended, the pair separated for lunch and Mr Kim returned to the North in a heavily guarded black limousine.
When he returned in the afternoon, the two leaders took part in a ceremony consisting of the planting of a pine tree using soil and water from both countries.
The pair shovelled soil on the roots of the tree and unveiled a stone marker featuring their names, official titles and a message that read: "Planting peace and prosperity."
Mr Kim arrived for the symbolic discussions on Friday accompanied by nine officials, including his powerful and influential sister Kim Yo-jong.
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