By Agence France-Presse
The Blue House, South Korea's presidential office, said the two leaders held talks for two hours in the truce village of Panmunjom, where they had met last month and made a declaration vowing to improve ties.
"They exchanged views and discussed ways to implement the Panmunjom Declaration and to ensure a successful US North Korea summit," the Blue House said in a statement, adding Moon would make a personal statement on Sunday morning.
On Thursday Trump cancelled his upcoming meeting with Kim which had been due to take place in Singapore on June 12 -- only to reverse course a day later and say it could still go ahead after productive talks were held with the North Korean oficials.
The original decision to abandon the historic summit blindsided South Korea which had brokered a remarkable detente between Washington and Pyongyang after months of Kim and Trump trading insults and threats of war.
Pictures released by the Blue House showed Moon shaking hands with both Kim and his sister Kim Yo Jong, who has played a major public role in recent talks with the South, including leading a delegation across the border during February's Winter Olympics.
The meeeting between Moon and Kim took place in a grand building on the North Korean side of Panmunjom, a surreal and heavily fortified village that lies between the two countries and marks the spot where the armistice ending the Korean War in 1953 was signed.