"We are not going to comment on the issue".
South Korea has welcomed Kim Jong Un's conciliatory gesture to Seoul as an improvement in inter-Korean relations that would lead to peace and stability on their peninsula. "It was done in hockey, so why not with us?" he said.
After delivering an invitation for Moon to visit Pyongyang earlier on Saturday, Kim arrived dressed in a black fur-collared coat and took her seat next to North Korea's ceremonial head of state Kim Yong Nam, with Olympic chief Thomas Bach also present.
Pence and the North Koreans have been an awkward presence at the Games to say the least.
Kim Jong-un wanted to meet Moon "at an early date", a spokesman for the Blue House said.
In stark contrast, two kinds of kimchi - the fermented cabbage that features in every Korean meal - were on the menu for the delegation's lunch with Moon at the Blue House on Saturday, one mild Northern style version and a spicier Southern recipe, along with soju, the traditional Korean rice liquor. The Pences, seated next to Moon and just a row ahead of Kim and the North's 90-year-old nominal head of state, remained in their seats, unsmiling.
Pence said the United States and South Korea were closely aligned in their approach to dealing with North Korea.
Pence shook hands with other leaders, including close ally Japanese Prime Minister Shinzo Abe, but not Kim Yong Nam, according to a Blue House pool official.
The two neighboring rival countries displayed an act of solidarity by having some participants from each country honored together during the opening ceremony, and combining the respective women's hockey teams into a singular, unified one.
When he insisted to Mr Moon that South Korea and the United States should resume their joint Foal Eagle military exercise after the Olympics, he was told not to meddle in the South's "sovereignty and internal affairs".
Vice President Mike Pence was at pains to insist that Washington and Seoul were on the same page as he returned to Washington from leading the US delegation to the Olympics.
The opening ceremony for the 2018 Winter Olympics began in Pyeongchang yesterday with a symbolic quest to find peace, which has become the overriding theme of these games.
"I am very confident, as President Trump is, that President Moon will continue to stand strongly with us in our extreme-pressure campaign", Pence told NBC in an interview, maintaining all options were open to deal with the crisis.
In its efforts to bring North Korea to the Pyeongchang Games, South Korea paused joint military exercises with the US and relaxed a series of sanctions, including on individuals like Ms. Kim.
The Winter Games, staged only 80km (50 miles) from the North Korean border, saw the two Koreas, who are technically still at war since a 1953 armistice, march together at the opening ceremony for the first time since 2006.