Earlier on Friday, Pence said Moon gave his backing to additional measures the United States is planning to try to curb North Korea's missile and nuclear programs, speaking after paying tribute at a South Korean memorial.
Athletes from both sides, technically still at war, marched together at the opening ceremony and have fielded a unified women's ice hockey team, the first time an inter-Korean team has competed at any Olympic Games.
Kim Yo-jong and the North's ceremonial head of state, Kim Yong-nam, made up the most senior delegation from Pyongyang o visit the South since the Korean War in the 1950s.
The North and the United States were also holding a series of high-level talks on Pyongyang's nuclear and missile programmes.
"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", said Pence's spokeswoman, Alyssa Farah.
In his meeting with Han, Moon expressed hope that China will play a bigger role in helping inter-Korean talks, which resumed with the Pyeongchang Olympics, lead to a Pyongyang-Washington dialogue.
USA vice president Mike Pence also attended the opening ceremony but had no contact with the North Korean delegation.
On Monday, Rep. Choo Mi-ae, the ruling party leader, welcomed the North's proposal. She and Kim Yong Nam were seated behind Moon and his wife, while Pence and his wife were seated beside the Moons and Japanese Prime Minister Shinzo Abe. The first step in this direction was the decision of joint marching of North Korean and South Korean athletes in the opening ceremony of the Winter Games and the declaration of the first joint Olympics team in Women's Ice Hockey.
"They fit in great with our team, and we're just trying to get them integrated as quickly as possible" said Brandt, a team assistant captain whose Korean name is Yoonjung Park.
Only 22 will dress to play Saturday night, leaving Murray the hard task of deciding whether to play any of the North Koreans or sit some of the South Koreans she has worked with for many weeks. If Moon accepts the invitation, then this would pave the way for what could be the third meeting of the inter-Korean summits between the two countries.
It would be the first summit in more than a decade between Korean leaders. For his part, Abe said that Japan and the U.S. had "confirmed... that we can never accept a nuclear-armed North Korea".
After the invitation was conveyed, a Blue House official said local authorities are now planning what message Moon will send to Kim Jong-un, and how he will send it, once the PyeongChang Winter Olympic Games wrap up later this month. They were also served North Korean-style fermented fish and white "kimchi" or fermented cabbage.
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