Speaking to reporters on his flight home on Saturday, Pence said the United States, South Korea and Japan were in complete agreement on isolating North Korea over its nuclear weapons program.
"Let us promote mutual conciliation and harmony through the power of sport".
Athletes from South Korea and the DPRK also marched together under a unified Korean flag at the opening ceremony of the 23rd Winter Olympics on Friday night, marking the first walking together in 11 years of the two countries' athletes under the same flag at the opening ceremony of an worldwide sports event.
Moon gave qualified consent to holding a future summit with Kim, the first between the two Koreas since 2007.
But the North was welcomed with open arms to what South Korean President Moon Jae-in called "Olympic games of peace".
The thaw in relations has centred on the Olympics, with a senior American member of the International Olympic Committee calling for the joint ice hockey team, which included 12 North Korean players, to be nominated for the Nobel Peace Prize.
"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. Rumors swirled Friday as the Koreans practiced that Kim Yo Jong, sister of North Korean leader Kim Jong Un, might attend the game and be among the capacity crowd of 6,000 at the Kwandong Hockey Center.
Moon and US President Donald Trump agreed via a telephone conversation on January 4 to postpone the joint annual war games during the Winter Olympics and Paralympic Games set to run from February to March.
Outside the stadium, there were anti-unification protests over North Korea's involvement in the games.
And on Friday, the sister of North Korean leader Kim Jong Un, Kim Yo Jong, became the first member of the North's ruling family to visit the South.
US Vice President Mike Pence said on Wednesday Washington would soon unveil its "toughest sanctions ever" on North Korea, adding that the regime in Pyongyang would not be allowed to "hijack" the upcoming Olympics.
North Korea has made clear that it does not intend to negotiate away its nuclear and missile programs in return for relief from global sanctions.
"The North Koreans should understand that for a summit or any kind of serious talks to occur, Moon needs to be able to take something to Washington - something that addresses denuclearisation", he said. A top North Korean official seemed to rule out a potential meeting with US officials in the North's state-run media on Thursday, but Pence suggested to reporters that it was still a possibility.
At the opening ceremony for the Games, Mr Pence, Kim Yo-jong and Kim Yong-nam were seated in close proximity to each other.
The team was created by adding 12 DPRK players to the existing South Korea's squad of 23 players. "When my eyes met the North Korean athlete's I just smiled".