Kim and his entourage including Kim Yo-Jong, the sister of North Korean leader, were welcomed by South Korean Unification Minister Cho Myoung-gyun at Incheon International Airport.
"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.
That's what makes Saturday's meeting so rare: Not only is Kim Yo Jong in the South for the first time ever, but she's chatting with South Korea's president inside the Blue House (South Korea's White House, so to speak).
The last summit meeting between North Korean and South Korean leaders took place in 2007, more than ten years ago.
"I hope the right conditions will be created so that the leaders of the South and the North will hold a meeting", he said.
The North Korean officials arrived here Friday as part of a 22-member delegation, led by the North Korean ceremonial head of state, Kim Yong-nam, who is the president of the Presidium of the Supreme People's Assembly.
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 visit of the North's high-ranking delegation, which concluded on Sunday (February 11), has fascinated the South Korean public.
The games are also being attended by North Korean leader Kim Jong Un's sister and other senior officials.
Opening Ceremony of the Winter Olympics Draws 28.3 Million Viewers
President Donald Trump and Supreme Leader of North Korea Kim Jong Un were not among those present. It's important not to overestimate the significance of all this.
As it turned out, with the two Koreas celebrating a moment of unity, the United States was left outmaneuvered by an adversary and out of step with an ally.
Washington seems to be unhappy about the Pyongyang-Seoul engagement.
"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".
The games have turned into an opportunity to cool tensions between the two Koreas, after initial doubt that North Korea would participate at all. Warmbier was jailed in North Korea for over a year after he was accused of tearing down a propaganda poster at the Yanggakdo International Hotel.
"On a political level in Seoul, there is no wedge that can be driven between us by North Korea", Mattis said, echoing comments made by U.S. Vice President Mike Pence.
And Pyongyang's official Korean Central News Agency focussed on the team and the North Korean cheerleaders rather than the 8-0 defeat - mentioning neither the outcome nor the score in its dispatch.
He also warned that Seoul's ready acceptance of Pyongyang's overtures could damage its alliance with the US.