Kim Yo Jong delivered a letter from her brother during a meeting with Moon on Saturday.
It marked the first time in eight and a half years that a high profile DPRK delegation visited South Korea's presidential complex. Three must be North Koreans, and head coach Sarah Murray has said she plans to use three or four North Koreans. His son, Otto Warmbier, died after being returned to the USA with extensive brain damage he suffered while being detained in North Korea.
"By sending the sister to South Korea and seeking a visit by the president, North Korea is probably trying to give the impression that it's taking the lead on dialogue", the source said. Moon also stressed the need for the U.S. to come to the table.
Japanese Prime Minister Shinzo Abe also attended the ceremony.
Coach Sarah Murray recalled pulling up for the game in Incheon and the crowd on the road outside split pretty evenly between people against the North Koreans joining the team and supporters waving flags showing the full Korean peninsula.
North Korean state media said Thursday there was no intention on the North Korean side for such talks to take place.
The pair were spotted in the crowd at Pyeongchang Olympic Stadium, and appeared to be getting along splendidly.
Moon said improved relations between the Koreas may be a step toward resolving the nuclear standoff.
The delegation will return to North Korea on Sunday.
The United States insisted it would continue its policy of exerting global pressure on North Korea in an effort to get it to abandon its nuclear program.
At Friday's opening ceremony, for example, Moon shook hands with Jong, as Pence, sitting merely feet away, looked stone faced, never acknowledging the North Korean delegation.
Kim Yong Nam on Friday took a picture with Moon and his wife Kim Jung-sook before entering the reception room. South Korean President has responded to the offer positively as reported by Korean Joongang Daily.
North Korea did prove it was capable of a charm offensive, a stark contrast from the past year when Kim Jong Un and President Trump have traded insults and dire threats.
Kim Yong Nam, the North's nominal head of state who was also at Saturday's meeting, said "even unexpected difficulties and ordeals could be surely overcome and the future of reunification brought earlier when having a firm will and taking courage and determination to usher in a new heyday of inter-Korean relations".
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