Moon apparently cited the conditions necessary for an inter-Korean summit. "Let us make it happen by creating the necessary conditions in the future," he was quoted as saying.
The South Korean President also stressed the need for the Communist North to resume its dialogue with the US. "An early resumption of dialogue between the US and the North is needed also for the development of the South-North Korean relationship," he said, according to his spokesman.
The figures from the two Koreas shared kimchi (Korean pickled cabbage) and soju rice liquor, and spoke for three hours.
Other members of the North Korean delegation present at Saturday's meeting included Ri Son Gwon -- who led the first sit-down talks at the Demilitarized Zone (DMZ) earlier this year, and Choe Hwi.
The meeting followed a brief encounter between the two parties at the Olympic Opening Ceremony on Friday, in which Moon twice shook hands with Yo-jong.
Pence, who is leading the US delegation to the Olympics, briefly encountered Kim Yong-nam at the Games but the two tried to avoid directly facing each other.
Later on Saturday, Moon and Kim Yong-nam will attend the first ice hockey match played by teams from both the sides, according to reports.
It was not immediately reported whether the North Korean leader's sister would attend the evening match against Switzerland.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)