And Pence repeated that USA policy remains that North Korea must give up its nuclear arsenal and stop trying to build ballistic missiles.
"Make no mistake about it, the United States of America has viable military options to deal with a nuclear threat from North Korea but, that being said, we hope for a better path", he said.
US Vice President Mike Pence snubbed the lunch and avoided any interaction with Ms Kim when they sat just feet apart at the spectacular opening ceremony. Moon's chief of staff held a farewell dinner for the delegation before the delegation attended a performance by a North Korean orchestra, the last item on their itinerary before heading home. US President Donald Trump and the North Korean leadership traded insults as tensions rose. He is entertaining a North Korean offer to visit Pyongyang.
Even though the human face appeared only briefly on TV screens, it triggered a rapid response on Twitter, with one tweet saying, "It may be considered an auspicious item in South Korea, but to be honest I was scared".
It would be the first meeting of leaders of North and South Korea since 2007.
The South's Unification Ministry said steps to improve ties would be led by the two Koreas, but with the support of the worldwide community.
Before leaving South Korea on Saturday evening, Pence watched short track speed skating games, with Fred Warmbier seated behind him.
"We should firmly keep in mind that any talks where denuclearisation is not a precondition only buy North Korea more time to complete its nuclear capabilities while they fool us with their peace offensive façade", said Chang Je-won, spokesman for the Liberty Korea Party. -North Korea meetings (or lack thereof) ignores what was going on beneath the surface.
In a fascinating development, North Korean leader Kim Jong Un's younger sister made a show of attending the Games' opening ceremonies this weekend in Pyeongchang, South Korea, along with her nation's ceremonial head of state, Kim Yong Nam.
The frame for the still-nascent diplomatic path forward is this: The United States and its allies will not stop imposing steep and escalating costs on the Kim Jong Un regime until it takes clear steps toward denuclearization. While both the naturalized and South Korean-born players used English words for basic ice hockey terms such as "shoot", "pass" and "change", the North Korean players did not use any English terms. "But if you want to talk, we'll talk".
The ongoing rapprochement mood flared after Kim Jong Un said in his New Year's Day address that he was willing to send an Olympic delegation.
Ms Kim, who is though to be about 30 years old, was promoted to the powerful politburo last year.
Kim Yo Jong and her delegation spent three days dining with top government officials, watching the opening ceremony and cheering for the united women's ice hockey team the two Koreas have fielded at this Olympics.