Kim Yo Jong, the North Korean leader's younger sister, and the other North Korean delegates, led by the 90-year-old head of state Kim Yong Nam, were feted at a lunch with South Korea's prime minister on Sunday before sitting next to South Korean President Moon Jae-in at the concert by North Korea's Samjiyon Orchestra in Gangneung, a city that is co-hosting the Olympics.
And Kim's sister, Kim Yo-jong, made history by becoming the first member of the North's ruling family to visit the South since the Korean War in the mid-20th century.
Vice President Mike Pence is cheering on US speed skaters at the Winter Olympics before departing South Korea for Washington on Saturday.
The isolated North sent hundreds of athletes, cheerleaders and other figures to cross the border to take part in the Games.
North Korea has made clear that it does not intend to negotiate away its nuclear and missile programs in return for relief from global sanctions.
The Korean Central News Agency reported that Kim Yo Jong delivered a letter and message from her brother during the meeting Saturday in Seoul, but did not mention that Kim Jong Un invited Moon to visit Pyongyang for a summit. Pence spoke in an interview on his way home from the Winter Olympics.
The invitation had sparked concern that Kim had succeeded in driving a wedge between South Korea and the US, which have differed on the best way to rid North Korea of nuclear weapons.
White House officials and other critics believe North Korea is trying to use the worldwide stage to gain sympathy and ease punishing economic sanctions and diplomatic pressure that are beginning to bite.
The vice president is not directly addressing the news.
Such a summit, if it came about, would mark the first time that leaders of the two Koreas have met since 2007.
Washington has pursued a strategy of exerting maximum pressure on Pyongyang through tough sanctions and harsh rhetoric, demanding it give up its pursuit of nuclear weapons first for any dialogue to occur.
Major protests have erupted in South Korea as activists burn the North's flag.
Moon has expressed hope the détente could lead to a broader dialogue with the United States.
The two Koreas, which remain technically at war since their 1950-53 conflict ended in an armistice instead of a peace treaty, have only had two previous summits.
Among those who participated in such meetings were the late leader and father of Kim Jong-un, Kim Jong-il, and the late former presidents of the South, Kim Dae-jung and Roh Moo-hyun, respectively.
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