The leaders met at the Joint Security Area of Panmunjom early Friday. The talks lasted nearly 100 minutes after starting at 10:15 a.m.
"At the summit, the two leaders held serious and honest discussions on ways to denuclearize the Korean Peninsula, establish permanent peace and develop South-North Korea relations," Yoon Young-chan, Moon's top press secretary, told a press briefing.
"They have agreed to continue working-level discussions to craft a joint declaration and once the declaration is made, the leaders will hold a signing ceremony and jointly announce it," he added.
Moon earlier said what was agreed upon at his summit with Kim will be a great present to the entire world.
"I believe it will be a great present to the people of the South and the North, people of the entire world as we had lots of great discussions today," he was quoted as saying as his closing remarks.
Kim too said their agreement may at least be a small gift to many.
"To those who expected much, it might only be the start, the tip of an iceberg, but once what we discussed today at the first meeting is announced, I hope it will offer at least some satisfaction to those who expected much," the North Korean leader said, according to Cheong Wa Dae.
Kim returned to the North Korean side of Panmunjom after his first meeting with Moon ended.
He was set to again cross the inter-Korean border later in the day for a series of events apparently aimed at forming a personal relationship between the leaders of the divided Koreas that technically remain at war.
Moon and Kim will jointly plant a tree to mark the first-ever inter-Korean summit held in South Korea, followed by a friendship walk, Cheong Wa Dae said earlier. The Moon-Kim meeting marked the third inter-Korean summit. The two previous summits in 2000 and 2007 were both held in Pyongyang.
Moon will then host a welcome dinner for the North Korean leader and his wife, Ri Sol-ju, who was set to arrive at Panmunjom at 6:15 p.m., according to Yoon.
Ri's attendance could be a sign of substantive progress at the summit as Cheong Wa Dae officials earlier said it was not clear whether she will come to the world's last remaining frontline of the Cold War, until as late as Friday morning.
Ri will hold brief talks with Moon's wife, Kim Jung-sook, before they both attend the official dinner, according to Yoon.
The meeting will be the first encounter between the first ladies from the two Koreas.
The dinner will also involve dozens of other North and South Korean officials and celebrities, according to Cheong Wa Dae spokesman Kim Eui-kyeom.
There will be a total of 26 North Korean officials, including Hyun Song-wol, head of the Samjiyon Orchestra that staged performances in South Korea during the 2018 PyeongChang Winter Olympic Games.
Moon and his wife will be joined by 32 South Koreans, including the chief of the ruling Democratic Party, Rep. Choo Mi-ae, and Cho Yong-pil, a famous South Korean singer who, along with some 100 other South Korean artists, traveled to Pyongyang earlier this month to reciprocate the visit by the North Korean orchestra.(Yonhap)