Earlier on Saturday, Kim invited Moon for talks in Pyongyang, setting the stage for the first meeting of Korean leaders in more than 10 years.
Moon was heard asking the visiting delegation "I appreciate you stayed late out in the cold, are you all well?" before the talks proceeded behind closed doors.
He's continuing his shenanigans at the Winter Olympics in Pyeongchang, South Korea.
Though Moon has used the Olympics to resurrect meaningful communication with North Korea after a diplomatic stalemate over its nuclear program, he didn't immediately jump on the North Korean offer for a summit.
The North's Alpine coach, Pyon Yong Do, says attending the Olympics has a "significant meaning" though winning competitions are important, too. "The last thing I'm anxious about is a North Korean propaganda success". He supported Pence's moves to meet with North Korean defectors, paying respects at a memorial to 46 South Korean sailors killed in a 2010 torpedo attack blamed on the North. Pence also invited as his Olympics guest the father of US college student Otto Warmbier, who died after he was imprisoned by North Korea for stealing a propaganda poster.
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Moving legislation swiftly through the upper chamber of Congress requires consent by all 100 members, but Mr Paul objected. Ryan has said he is willing to address the future of young immigrants but has not laid out an exact timeline.
During Sunday's lunch at the Walkerhill Hotel, Prime Minister Lee told the North Korean delegation he hoped the "right conditions" would be created for the two heads of state to meet, an official from Lee's office said. "But the Olympic moment that President Moon is trying to generate here is not a time to nurse those grievances", Jannuzi said.
During their meeting President Moon was pictured smiling and shaking hands with Kim Yo Jong.
South Korean participants included senior officials Jeong Eui-yong, Jo Myong-gyoon and Im Jong-suk - the chief presidential secretary. He also called for the need of a quick resumption of dialogue between North Korea and the United States.
Tensions between the two soared past year as Pyongyang launched intercontinental ballistic missiles capable of reaching the United States mainland and carried out by far its most powerful nuclear test to date.
But the pinnacle of Pence's messaging was at the opening ceremony itself, where his personal guest was the father of American student Otto Warmbier, who died a year ago after being returned home in a coma after his 17-month detention in North Korea.
On page two it printed seven more of the opening ceremony and its representatives' meetings and handshakes with Moon, whom it described as president. Jo Yong Sam, department director general of North Korea's foreign ministry, said Thursday the country had never "begged the USA for dialogue" and wasn't about to start now. In 1999, the two Koreas played friendly basketball matches in Pyongyang and Seoul after ground was broken for an arena Chung donated in the North Korean capital.