Moon joined Pence in the arena and sat next to him, turned around to greet Warmbier, according to a White House pool report.
The US has repeatedly pressed China, North Korea's most significant trading partner and main ally, to do more to rein in Pyongyang's nuclear and missile ambitions.
The vice president and North Koreans are not expected to interact Saturday during events in Pyeongchang, according to a second US official.
In dispatching the highest level of government officials the North has ever sent to the South, Kim Jong-un revealed a sense of urgency to break out of deep diplomatic isolation in the face of toughening sanctions over his nuclear program, analysts say.
Pence and his people had essentially no comment on that significant development as Pence left South Korea later in the day.
Make sure that as north Korea engages in what prime minister Abe rightly called a "charm offensive" around the Olympics.
"President Moon responded by saying that the two sides should work on establishing the right conditions to realise the meeting", the South Korean spokesman Kim Eui-kyeom said.
Turns out the North Korean leader is actually an Australian named Howard.
A damaged statue of North Korean leader Kim Jong-un is seen in front of Deoksu Palace in Seoul on Feb. 10 2018
Olympic officials on Sunday, February 11 said a cyberattack was responsible for an internet and wifi shutdown during the Pyeongchang Winter Games opening ceremony, but refused to say who was responsible.
Pence avoided the North Korean official entirely.
The South Korean president requested both that North Korea re-open dialogue with the USA, and that the Koreas hold talks.
"The 2000 summit was held after the so-called "Perry Process", a 1999 proposal for a three-stage resolution to North Korea's weapons of mass destruction".
Kim Yo Jong, the younger sister of Kim Jong Un, "courteously" handed over a personal letter from the North Korean leader to Moon during talks on Saturday and also told Moon of her brother's "intention", KCNA said, without elaborating on what that was.
Some North Korean experts believe tough United Nations sanctions that are cutting off most of the isolated North's sources of revenue have added pressure on Pyongyang to engage further with Seoul. He's been very clear what his message is.
Fred Warmbier attended the ceremony as Pence's guest, but in the US delegation box.
If the attack does indeed turn out to be Russian in origin, then it could impact the International Olympic Committee decision over whether to lift the country's suspension before the Closing Ceremony and allow athletes to march under their own flag there.
The Winter Olympics opening ceremony aired Friday night on NBC.