"We are determined to make sure that even in the midst of the powerful background & idealism of the Olympics, the World is reminded of the truth about North Korea", Pence tweeted on Friday.
Pence told reporters that the two leaders "spoke as friends" during his visit to South Korea, and their discussions including the meeting between Moon and the North Korean delegation, led by Kim Jong Un's sister, Kim Yo Jong.
All broke out in broad smiles.
Any summit between the two still-officially warring Koreas would be a coup for Moon, who has been pushing for a diplomatic solution to the standoff over North Korea's nuclear and missile programmes.
North Korean media lauded the players and supporters of the unified Korean women's ice hockey team Sunday (Feb 11) after their first match at the Olympics - without mentioning their 8-0 drubbing.
Moon's desire to engage North Korea was in contrast to his U.S. ally.
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.
South Korean presidents Kim Dae-jung and Roh Moo-hyun went to Pyongyang in 2000 and 2007 respectively to meet the current leader's father and predecessor Kim Jong Il. There was another handshake.
The North Korean artists performed Thursday in Gangneung, a coastal city that will host the skating, hockey and curling events during the games, and are to perform again in Seoul.
Tensions between the two soared past year as Pyongyang tested missiles capable of reaching the US mainland and its most powerful nuclear device to date, while Kim Jong Un and US President Donald Trump traded personal insults and threats of war.
The invitation puts Mr Moon in a hard position as he had promised to engage with the North, but his U.S. ally is cautious of Seoul falling for North Korea's charm offensive. For good reason, both harbor pretty deep distrust of the North.
A senior USA official said Pence and Moon, while watching speed skating together on Saturday night, discussed intensifying sanctions.
"I like the idea of unification and I think it's nice that North Korea's going to participate in the Olympics but I haven't really thought about unification".
It was the first time a member of North Korea's ruling family ever visited the presidential palace, called the Blue House. "President Moon would have run with it and Kim Jong-un would have maximized the South's enthusiasm".
At the opening ceremony Friday night, Pence was seated in front of Kim Yo Jong, Kim Jong Un's sister and part of the North Korean delegation.
Some North Korean experts believe tough United Nations sanctions that are cutting off most of the isolated North's sources of revenue have added pressure on Pyongyang to engage further with Seoul.
The Soviet Union occupied North Korea and the United States occupied the South, separating the two territories by the 38th parallel.
A total of 50,000 North Koreans are expected to courageous freezing temperatures, including people trained in a mass-choreographed card performance, according to the report. After a photo together, each of the Koreans shook hands with the three men while Kim Jong Un's sister watched.
Now, South Korea's allies must decide whether to stand back and allow Moon to pursue his policies of reconciliation, or put the screws back on to Pyonyang.
Many experts say Kim's overture is meant to use improved ties with Seoul as a way to weaken US -led global sanctions toughened after its series of big weapons tests a year ago that include its sixth and largest nuclear test explosion and three intercontinental ballistic missile launches.
Kim Yo Jong is scheduled Saturday to have a luncheon with Moon Jae-in, details of which have not been made public. Just a few days later, she is the face of North Korea at PyeongChang.
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