Following the visit that lasted nearly three hours, Seoul's Presidential Spokesman Kim Eui-kyeom told reporters that the North Korean leader's sister delivered the message to Moon that Kim Jong-un would like a meeting.
But a bonus was the North Korean "army of beauties", or "cheerleaders" as they've been dubbed - a group of 230 women attending to cheer on the North Korean delegation at this year's Games.
North Korean defector Ji Seong-ho met and embraced Fred Warmbier, father of Otto Warmbier - the United States student who died days after his release from a North Korean prison. The daily said the two sides "discussed a range of issues concerning the two Koreas".
"I am very confident, as President Trump is, that President Moon will continue to stand strongly with us in our extreme-pressure campaign [against North Korea to give up nuclear weapons]", Pence said later.
U.S. Vice President Mike Pence and his wife arrived after the handshakes.
Moon joined Pence in the arena and sat next to him, turned around to greet Warmbier, according to a White House pool report.
Moon met Kim Yo Jong - a close confidante of her brother and the first member of the dynasty to set foot in the South since the Korean War - and the North's ceremonial head of state Kim Yong Nam at the Blue House in Seoul. Kim Yo-jong's visit to the South also marks the first time a member of North Korean founder Kim Il-song's family has crossed the inter-Korean border since the end of the 1950 Korean War.
Moon has expressed his intention to use the Winter Olympics as a chance to make diplomatic inroads with the North and restore normalcy, following months of high tensions on the Peninsula.
The South Korean president in response proposed to work together to create an environment that is conducive for inter-Korean talks in North Korea. The two will be attending the opening ceremony, where a North Korean delegation will also be present.
His office said he did not interact with the North Koreans. The senior USA official said Pence was not trying to avoid the North Korean officials but rather ignore them.