Prior to the opening ceremony on Friday night, Pence arrived late to a dinner reception between the two Koreas and greeted everyone at a main table except for Kim Yong Nam, North Korea's nominal head of state, Reuters reports.
The handwritten invitation to President Moon was delivered by Mr Kim's influential sister, Kim Yo-jong, at a landmark meeting in the presidential palace in Seoul, as the Games opened on Saturday.
Throughout the ceremony there were constant winks to peace, such as the theme "Imagine" by John Lennon, an ode to coexistence, sung by four well-known South Korean singers.
He didn't say what those conditions were, but he urged North Korea to open a dialogue with the United States, suggesting no diplomatic progress could be made without USA participation.More news: Safe return needed for Rohingya refugees - Johnson
"Good job", Bach and President Moon said to the players, shaking hands one by one with all of them.
The two leaders however, did not discuss North Korea's invitation to Moon to visit Pyongyang, according to a senior administration official.
Later, Pence echoed the tough stance being taken by Donald Trump against Kim Jong Un's continued nuclear tests. In a speech that Kim gave on New Year's Day, in which he first raised the possibility of the North participating in the Olympics, he vowed to "mass-produce" nuclear weapons and missiles.
The North's official Korean Central News Agency also referred to Moon as president.
Two South Korean presidents, both of them progressives, have gone to Pyongyang for summits before, both with Kim Jong Un's father.More news: South and North Korean athletes unite during opening ceremony in Pyeongchang
"There is no daylight between the United States, the Republic of Korea, and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear ballistic missile program", Pence said in comments carried by CNN. She was photographed sitting behind Vice President Mike Pence during the ceremony.
She is considered the gatekeeper of her brother's appearances and security, according to Michael Madden, the founder and director of NK Leadership Watch, an analysis website focused on North Korea.
It was not immediately reported whether the North Korean leader's sister would attend the evening match against Switzerland.
"What we'd like to achieve, by coming to South Korea... is to show the world that this is what peace could look like when two leaders get along", Howard told the paper.More news: Heading home, Pence insists 'no daylight' on North Korea
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