Pence left an Indianapolis Colts game that he was attending past year minutes after the national anthem after players from the opposing San Francisco 49ers knelt in protest during the national anthem, a move that sparked criticism from NFL players and Democrats.
"I am willing to meet with President Moon in the near future", Kim Yo-jong quoted Kim Jong-un as saying, according to presidential spokesman Kim Eui-kyeom.
Aides did not immediately say whether the invitation was discussed as the two sat next to each other viewing several race heats Saturday.
The South Korean presidential office said Mr. Moon had encouraged North Korea to have dialogue with the U.S.as well.
Pence was scheduled to leave for the United States on Saturday night. This was more about finding a sliver of hope in relations between the two bitter rivals than it was about chasing dreams of Olympic glory.
Moon and the DPRK delegation shared a view that the two Koreas should keep a good atmosphere of reconciliation and peace on the peninsula while boosting talks, exchange and cooperation between Seoul and Pyongyang.
Pyongyang conducted its largest nuclear test previous year and in November tested its most advanced intercontinental ballistic missile that experts said has the range to reach anywhere in the United States.
The 2018 Winter Olympics officially began Friday when a parade of athletes entered the Olympic stadium, including athletes from North and South Korea who marched together behind a blue and white Korean unification flag.
Seoul hosted the 1988 Summer Olympics, which Pyongyang boycotted, and also bombed Seoul-bound Korean Air Flight 858. US Vice President Mike Pence, sitting a few seats away in the same Opening Ceremony VIP booth, looked stony faced as the scene unfolded.
Following the meeting, Pence press secretary Alyssa Farah said in a statement, "The Vice President is grateful that President Moon reaffirmed his strong commitment to the global maximum pressure campaign and for his support for continued sanctions".
"North Korea seems to have no intention of abandoning its nuclear (program)", a Japanese government official said.
It's worth noting that Fred Warmbier, the father of Otto Warmbier who died after being held captive in North Korea, met with Pence in PyeongChang earlier in the day.
Lim's victory in the 1500m short-track speed skating event gave South Korea their 22nd gold medal in the sport since it made its debut in 1992.
The colorful opening ceremony kicked off what will be the biggest Winter Olympic Games in history with more than 2,900 athletes from 92 countries competing.
Since a truce stopped the Korean War in 1953, contact between North and South Koreans has been rare, but every year hundreds of North Korean defectors cross into the South. Japan's focus is now likely to be on fortifying trilateral cohesion with South Korea and the United States.
"It's a breakthrough", said Michael Breen, the author of Kim Jong-il: North Korea's Dear Leader.
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