President Moon hosted Kim at the presidential mansion for lunch on Saturday - a session in which Kim extended an invitation for Moon to visit North Korea later this year.
Reviving inter-Korean talks is key to the polices of Moon, who says South Korea should be in the driver's seat in global efforts to deal with the North's nuclear threat.
In an extraordinary show of unexpected unity, North and South Korea sat side by side Friday night under exploding fireworks that represented peace, not destruction, as the 2018 Winter Olympics opened on a Korean Peninsula riven by generations of anger, suspicion and bloodshed.
That is the assessment of a former South Korean government minister and political experts who say the North has used the Games to drive a wedge between South Korea and its US ally and to potentially ease pressure on its sanctions-crippled state.
Hundreds of anti-North Korea protesters scuffled with riot police hours not far from the main stadium before the opening ceremony was due to begin. "Putting in real effort is our people's wish". "Eat your heart out, Pence", Kenworthy wrote.
"I hope the Olympics can be an opportunity for more negotiations and reunification", said Won Sik-shin, an elderly audience member who was awarded tickets to the concert through a senior citizens' association.
Flanked by a pair of F-35 Lightning II stealth fighters inside one of Yokota's massive hangars, Pence got a warm welcome to the stage from U.S. Forces Japan commander Lt. Gen. The other goal for Pence's appearance was to see Moon for a final time, forging one more photo op of the two, in light of the events of the day.
As part of his push against North Korean propaganda, Pence attended the short track speed skating with Fred Warmbier, the father of an American student who died previous year after being imprisoned in North Korea for 17 months.
Kim extended the rare invitation to the South Korean leader through his closest confidante: his only sister Kim Yo Jong, who was visiting the South as part of the North Korean delegation to the Winter Olympics, according to South Korea's presidential office on Saturday.
However, no member of North Korea's ruling family has ever before visited the Blue House, which is near where North Korea founder Kim Il Sung - Kim Yo Jong's grandfather - sent dozens of commandos to assassinate former South Korean military strongman Park Chung-hee in 1968.
The first medals of the Pyeongchang Olympics will be awarded Saturday, but most attention will be focused on a preliminary round hockey match featuring the combined Korean women's hockey team.
Moon is eager to use Kim's presence at the games to restore regular communication with North Korea and eventually pull it into nuclear talks.
To help prevent this outcome, and with Kim refusing to discuss denuclearisation with his "brethren" in the South (at whom he claims his missiles are not aimed), Moon now must figure out how to build up the intra-Korea dialogue to enable talks between North Korea and the US.
The North Korean diplomatic initiative comes amid growing global pressure, led by the United States, aimed at imposing maximum economic and diplomatic pressure on the regime.
"I came here to the South by crossing the border twice. So the question is, when are they going to hear that?"
Athletes from South and North Korea marched behind the blue-and-white Korean unification flag at the opening ceremony on Friday. Could they meet? That and other theories have engulfed South Korean media. "The world cannot turn a blind eye to the oppression & threats of the Kim regime".
But Pence said that Moon shared "a bit" about his meeting with the North Koreans, and that he "appreciated him sharing his perspective on that".