North Korean leader Kim Jong Un salutes during a visit to the Ministry of the People's Armed Forces on the occasion of the new year, in this undated photo released by North Korea's Korean Central News Agency (KCNA) on Jan 10, 2016.
The games have not reduced the USA -led global pressure on North Korea to give up its nuclear and long-range missile program that is threatening America and the world.
Pence said Friday that the USA would oppose talks between the two Koreas until the North agreed to open negotiations on ending its nuclear program.
Kim Yo-jong, the sister of leader Kim Jong-un, became the first member of the Kim dynasty to travel to South Korea, where she conveyed during a meeting an invitation for president Moon to meet in Pyongyang with the North Korean leader.
"By virtue of her family ties, Kim is among the most credible interlocutors that North Korea could have sent", said Christopher Green, a senior adviser on Korean affairs at the International Crisis Group think tank.
They have shared kimchi and soju with Moon, sat in the same box at the Olympics opening ceremony and cheered a unified women's ice hockey team together.
North and South Korea celebrate peace through taekwondo show
If taken up it would be the first time in a decade that the leaders of both countries have met for a summit. Others chanted 'Let's tear Kim Jong-un to death!' while tearing up a picture of the North Korean leader.
Mr Moon and Mr Kim's sister will have another opportunity to talk when they attend the final performance of a visiting North Korean orchestra on Sunday evening in Seoul.
Contrarily, North Korea has been raising the pitch on its missile development game plan.
"We're going to continue to put all the pressure to bear economically and diplomatically, while preserving all of our military options to see that that happens", Pence said.
US Secretary of State Rex Tillerson said in December the US was ready to talk without preconditions, only to have the White House nix the notion.
It remains uncertain whether such drills would interrupt potential plans for a third ever inter-Korean summit - the last of which was held in 2007.
The Games have triggered rapid reconciliation between the two Koreas, who are still technically at war.
The delegations shared a lunch of dried pollack dumpling soup, a regional specialty of the only divided province on the Korean peninsula, and soju, a spirit popular on both sides of the heavily militarized border.