The discussions from Saturday's meeting weren't immediately released.
Moon has already put a summit offer on the table.
She is reportedly the first member of Jong-Un's family to travel South across the border since the Korean War.
Pence travelled to South Korea to lead the US delegation to Friday's opening ceremonies, but has used his trip to participate in symbolic events meant to shine a spotlight on North Korea's nuclear program and human rights abuses.
This items corrects that Kim Yo Jong is the leader's sister.
The officials said it was fair to say both Pence and the North Koreans rebuffed South Korean President Moon Jae-in's efforts to facilitate a meeting between North Korea and the US.
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Saturday's visit marked the first time in eight and a half years a high-level North Korean delegation has come to the presidential office in Seoul. They were stopped and most were killed near the palace, which was newly rebuilt in 1991.
At a glittering but sub-zero ceremony, South and North Korea brought the crowd to its feet as they entered behind the blue-and-white Korean unification flag.South and North Korea last marched together at the 2006 Winter Olympics in Turin.
The differences are particularly challenging for women ice hockey players from the two Koreas who were asked just a few weeks ago to compete as one nation, the Canadian head coach of the joint team, Sarah Murray, told a news conference on Sunday. President Moon met with his Japanese counterpart, Prime Minister Shinzo Abe on Friday afternoon.
Choi Bok-mu, a fitness club manager at the Olympics athletes village in Gangneung, said he had not experienced any problems communicating with North Korean athletes, despite them speaking in a markedly different accent.
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As if to drive the point home, Kim Jong Un used the eve of the Olympics to throw a massive military parade in Pyongyang that was highlighted by several huge intercontinental ballistic missiles rolled out in launcher trucks.
Pyongyang conducted its largest nuclear test past year and said it had developed a missile capable of carrying a warhead to the United States.
Moon hoped to use the Olympics to ease tensions and North Korea agreed to send high-profile officials as well as athletes. Pence carried a similar message during his trip to Japan and South Korea.
North Korea, meanwhile, has shown no signs of abandoning its nuclear and missile programs, maintaining its hostile posture toward Washington.
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However, some individual Russian athletes will be allowed to participate in the Games by competing under a neutral Olympic flag. NBC said a full Total Audience Delivery for the games will be released later in the day.
Shivering athletes and spectators are bracing for one of the coldest Winter Olympics on record, with real-feel temperatures plumbing minus 10C at the opening ceremony.Japan's speed skaters are among the athletes who decided it was too cold to courageous the open-air ceremony, while organisers handed out heat packs, blankets and hats to keep spectators warm.