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The meeting began shortly after 11 AM on Saturday, the day after the delegation arrived in South Korea ahead of the opening ceremony of the PyeongChang Winter Olympics.
It cemented what has been a rapid improvement in Korean ties since North Korea - after months of fierce nuclear rhetoric and missile tests - agreed last month to attend its first Olympics in the South. Another focal point is whether Kim Yo Jong has any message for Moon from her brother.
As ever, its front page lead story was on the activities of leader Kim Jong Un - in this instance, being given a gift by Zimbabwe's visiting air force commander.
The spokesman says Moon replied that the North and South should continue to work to build conditions so that a summit can take place.
Moon's office says Kim's sister, Kim Yo Jong, came to the South as his special envoy.
"Pyeongchang Olympics will become the hope and light for everyone that hopes for peace, not only on the Korean peninsula but in northeast Asia and the entire world", said Lee.
The officials toasted with the Korean liquor "soju" and were served buckwheat and potato pancakes, dried pollock soup, grilled halibut and other dishes.
Inside, it had seven more pictures of their meetings with Moon and the opening ceremony in Pyeongchang - four of them featuring the South Korean leader, who was described as president.
South Korean President Moon Jae-in shook the hand of a smiling Kim Yo Jong, the powerful sister of North Korean leader Kim Jong Un, as he entered the VIP seating section, and again as the Korean athletes marched.
Moon is joined by his national security director, intelligence chief, chief of staff and the unification minister.
South Korean media have been closely covering the delegation, especially the moves and facial expressions of Kim Yo Jong.
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