He also noted that the two Koreas had agreed to submit a joint bid to host the 2032 Olympics.
The 2032 Olympic declaration might also be welcomed by the International Olympic Committee, which - given the massive expenses shouldered by single nations hosting global sports events, with their requirements for infrastructure spend - favors joint hostings.
"We can take military measures to achieve the goal of the "armistice agreement" by making the demilitarized zone into peace zone for the first time in 65 years", the defense ministry said in a separate statement.
The Korean leaders' summit meeting in Pyongyang, the North Korean capital, was their third, and it was Moon's first visit to Pyongyang as South Korea's leader. He didn't indicate in his brief remarks whether the US would be willing to take further steps to encourage North Korean action on denuclearization.
Moon and Kim have just wrapped up a joint summit in the North Korean capital of Pyongyang.
The question hovering over their talks this week has been whether Kim would agree to take steps to convince Washington that he is willing to denuclearize.
Moon on Wednesday acknowledged, "there will be challenges and trials, but the more we overcome them the stronger we will become".
Kim and Moon earlier smiled and chatted as they walked down a hallway and into a meeting room to finalize the joint statement, which also said that the leaders would push for a Korean Peninsula without nuclear weapons and to "eliminate all the danger of war".
At their talks the previous day, Kim thanked Moon for his role in coordinating the historic summit in Singapore, indicating his eagerness to continue talks with Washington. By committing to taking additional denuclearization measures, Kim appears to be trying to reopen negotiations with Trump. The two Koreas are still technically at war 65 years after an armistice ended the Korean War.
The two Koreas committed on Wednesday to "completely cease all hostile acts against each other in every domain, including land, air, and sea that are the source of military tension and conflict" - also agreed to in April's Panmunjom Declaration.
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Kim Jong-un vows to denuclearise at historic summit with South Korea
But experts said the document only contained vague promises that would do little to curb the North's nuclear program. North Korea's May Day Stadium is the largest in the world with a reported capacity of 150,000.
South Korean officials say the comprehensive military agreement signed Wednesday will create a permanent peace zone on the peninsula.
Though not directly linked to security, the leaders' announcement that they would seek a joint Summer Olympics was a significant move in terms of easing tensions and building trust.
The concessions, to be sure, are not particularly costly for North Korea and do not set it on the path towards nuclear disarmament, but will bear particular significance in their ability to reinvigorate the stalled diplomatic process between South Korea's ally, the United States, and North Korea.
On the issue of families separated by the Korean War, the two leaders agreed to open visiting centers where divided families could be reunited with their loved ones.
If carried out, it would be the first time that the North's highest leader has set foot in the South's capital since the division of the Korean Peninsula, something that has always been considered almost unthinkable in the South.
But his visit was criticized by U.S. Senator Lindsey Graham who said it risked undermining the U.S. policy of "maximum pressure" aimed at leaving Pyongyang little choice but to abandon its nuclear and missile development programs.
Although Trump has remained optimistic about improved relations between Washington and Pyongyang, the initial euphoria following the Singapore summit in June - after which the president declared that North Korea was "no longer a nuclear threat" - quickly wore off.
Moon expressed hope that talks would resume between North Korea and the US. "It is a very meaningful achievement".
But discussions over how to implement the vague commitments have since faltered and North Korea has consistently refused to give up its nuclear arsenal unilaterally.
Reflecting on his agreements with Moon, Kim remarked the "world will now see what the Korean people will make of their own future" in a departure from a past marked "by suffering and agony" due to division. In high praise of Kim, Moon continued that Kim had "answered the wishes of the Korean people and the world".