"An early resumption of dialogue between the United States and the North is needed also for the development of the South-North Korean relationship", Moon said, according to his spokesman.
Obviously, Miss Kim Yo-Jong, she is the younger sister of Kim Jong-Un that the leader of North Korea has a very close personal relationship with the North Korean top leader and therefore her visit bears special meaning to South Korea.
At the opening ceremonies on Friday, Pence sat stone-faced in his seat as Moon and North Korean officials stood together with much of the stadium to applaud their joint team of athletes.
"I think this overture towards South Korea is partly sanctions-related, and also related to the fact that it's clear a divergence has developed between Washington and Seoul's most keenly desired goals in the near term", said Andray Abrahamian, a research fellow at Pacific Forum CSIS in Hawaii.
"We get along personally, so I believe that Donald Trump and Kim Jong-un, if they talked they'd probably get along". The South Koreans want to use the Olympics to ease tensions spurred by North Korea's pursuit of nuclear weapons. The North Koreans left written messages in the Blue House's guest book.
She was joined in the meeting by Kim Yong Nam, another influential North Korean official, and wore a pin with the images of her father and grandfather - the North's previous leaders. A lessening of hostility between the two Koreas could, therefore, benefit America as well.
Cheerleaders from North Korea let rip in support for Choe Un Song but he was eliminated in the 1,500m heats and the 25-year-old failed to qualify for the semi-finals.
"He was going to leave immediately after taking the group photo session but President Moon urged him to "see friends" so he dropped by the reception venue briefly".
"Working in unity on the way to unification", Kim Yong-nam wrote.
He also reiterated the Trump administration's stance that the United States would take whatever "action is necessary to defend our homeland", including military operations, as it seeks to denuclearise the North.
After North Korea stalled for months before even announcing that it would take part in the Pyeongchang Olympics, the Games have turned into an occasion for a stunning rapprochement on the Korean peninsula.
But the United States and Japan have warned against North Korea's "smile diplomacy", through which Pyongyang is apparently trying to weaken worldwide economic sanctions against it by getting close to South Korea.
At a Friday VIP reception for delegation leaders, Pence arrived late and stayed for just five minutes - and did not interact with the delegation from the North.