It would be the first summit between the leaders of the two Koreas in more than a decade.
South Korean President Moon Jae-in talks with President of the Presidium of the Supreme People's Assembly of North Korea Kim Young Nam and Kim Yo Jong, the sister of North Korea's leader Kim Jong Un, during their meeting at the Presidential Blue House in Seoul, South Korea, February 10, 2018.
Her presence helped the theme of Korean unity to dominate the opening ceremony as the two Koreas marched under one flag.
Pence said Moon updated him about the meeting he had with North Korean officials and "both of us reiterated to each other tonight that we will continue to stand strong and work in a coordinated way to bring maximum economic and diplomatic pressure to bear on North Korea".
U.S. President Donald Trump and the North Korean leadership traded insults and threats of nuclear war as tensions rose, with Trump repeatedly dismissing the prospect or value of talks with North Korea.
It was the US that appeared to be the one left in the cold, especially after the sister of the North Korean dictator extended an invitation from her brother for Moon to visit the North.
Lee made the remark during lunch with a high-level North Korean delegation, including the North Korean leader's sister and special envoy, Kim Yo-jong, and the country's ceremonial head of state, Kim Yong-nam.
Any meeting would represent a diplomatic coup for Moon, who swept to power previous year on a policy of engaging more with the reclusive North and has pushed for a diplomatic solution to the standoff over North Korea's nuclear and missile programme.
Pence said he would seek to counter North Korea's attempt to use the Olympics for propaganda and invited the father of Otto Warmbier, an American student who died past year after being imprisoned in North Korea for 17 months, to the Games in Pyeongchang.
Already there have been concerns that North Korea's overture of the sports diplomacy is an indirect attempt by the regime to wedge a rift between the United States and South Korea.
"The grievances that the world has about North Korea are very legitimate".
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After the opening ceremony, the North Korean delegates moved to Seoul and spent the night at the Walkerhill hotel, a riverside facility named after late U.S. Army commander Walton Walker, who's considered a Korean War hero in the South.
At the game's end, the crowd cheered for the Korean team, which will play in another preliminary round against Sweden on Monday.
"We hope that President (Moon) could leave a legacy that would last over generations by leading the way in opening a new era of unification", she said.
For now, America seems unlikely to come to the negotiating table with North Korea at the Olympics.
The unified hockey team representing North Korea and South Korea didn't fare so well in their first outing, losing 8-0 to Switzerland.
"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 and ballistic missile programme", Pence told reporters during the return flight to the United States.
An editorial in the Yomiuri Newspaper read: "What can not be overlooked is that Moon did not directly demand North Korea to abandon its nuclear development". A big one could be a demand to cease the U.S.
Pence said Friday the USA would oppose talks between the two Koreas until the North agreed to open negotiations on ending its nuclear program.
The North is a notoriously tough negotiator, adamant that it needs its "treasured sword" of nuclear weapons to defend itself against the threat of invasion by the United States, and will never give them up.
"It seems clear", he said, "that the countries have entered a phase of restoring a regular level of contact".