Pence, speaking to reporters aboard Air Force Two after attending the opening ceremony of the Games in Pyeongchang, South Korea, said that he and President Moon Jae-in "continue to stand strong" and coordinate efforts against the North.
In Pyongyang, North Korea's official Rodong Sinmun newspaper also reported on the Games bonhomie, publishing photos of its ceremonial head of state clinking glasses with Moon and of the South's leader also shaking hands with a telegenic Kim Yo Jong.
Pence shied away from public criticism of Moon when they met Thursday evening, congratulating South Korea on hosting the games and pledging continued support in addressing the North's nuclear threat.
Kim Yo Jong told Moon that relations would improve quickly once he meets with her brother.
"For our team meetings it is going through to English to South Korean to North Korean".
The Games have triggered rapid reconciliation between the two Koreas, who are still technically at war.
Pence trip began in Japan, stopped in Seoul, and culminated with his visit to the Pyeongchang Winter Olympics opening ceremony.
Any meeting would represent a diplomatic coup for Moon, who swept to power past 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.
As controversial as it may seem, especially after her spectacular appearance at the Olympics, the US Treasury Department had blacklisted the "First Sister" in January 2017, adding her to the Specially Designated Nationals List for "severe human rights abuses" in North Korea.
Some set a North Korean flag on fire before police intervened, and others chanted "Let's tear Kim Jong-un to death!" as they ripped up posters bearing his portrait.
He has met with some North Korean defectors while there.
The younger sister of North Korean leader Kim Jong-un made history Friday when she paid an unprecedented visit to South Korea during the opening ceremony of the 2018 Winter Olympics.
The Trump administration has discouraged South Korea from engaging with the North, which has been subjected to increasingly tough global sanctions, unless it shows clear signs of giving up its nuclear weapons programme.
It would be the first summit in more than a decade between Korean leaders. Jo Yong Sam, department director general of North Korea's foreign ministry, said Thursday the country had never "begged the USA for dialogue" and wasn't about to start now.
Earlier, Moon warmly greeted North Korea's 90-year-old nominal head of state, Kim Yong Nam, as they attended the VIP reception.
Kim Yo Jong, viewed as one of the closest aides to her brother, and Kim Yong Nam held rare talks with Moon on Saturday, during which she delivered a personal letter from her brother requesting that the president visit Pyongyang at an early date.