Moon hosted the elderly Kim Yong Nam - technically the highest-level Northern official ever to go to the South - and Pyongyang's star representative Kim Yo Jong at the presidential Blue House.
According to South Korea's presidential Blue House, Moon responded: "Let us make preparations to realize the meeting".
The last summit was held in October 2007 between Roh Moo-hyun and Kim Jong-il, the father of the North Korean leader.
When he was returned to the USA, he had horrific brain injuries which his family attributed to him being tortured by the Kim Jong Un's regime.
But this news won't be welcomed in the United States, which wants the South to take a much harsher line against Kim and his regime - including demanding that it gives up its nuclear weapons program.
He also did not shake hands with Kim Yong Nam while making a brief appearance at a leaders' reception ahead of the ceremony - although Japanese Prime Minister Shinzo Abe, whose country is also regularly threatened by Pyongyang, did so, while exchanging pleasantries with the North Korean.
"It is absolutely necessary for the North and the United States to engage in talks at an early date", he cited Moon as saying.
U.S. Vice President Mike Pence and his wife arrived after the handshakes.
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.
U.S. Vice President Mike Pence is not directly addressing news that North Korean dictator Kim Jong Un has invited South Korean President Moon Jae-in for a visit, as the two Koreas use the Olympics as an opportunity for renewing ties.
What to expect at the 2018 Winter Olympics
Sochi 2014 hosted the inaugural Olympic team event when Russian Federation won the gold medal followed by Canada and the USA. She is still relatively inexperienced when it comes to worldwide competition, however, she is favored to earn a medal.
Experts say her visit for the Winter Games is calculated to answer the expected presence of Ivanka Trump at the closing ceremonies.
The vice president also met with North Korean defectors while in Pyeongtaek.
Donald Trump has begged a lot of comparisons with the head of North Korea, from their mutual love of military parades to their at best apathetic attitude to free society in general.
Pence said Moon updated him about the meeting he had with North Korean officials and "both of us reiterated to each other tonight that we will continue to stand strong and work in a coordinated way to bring maximum economic and diplomatic pressure to bear on North Korea".
The recent detente, anchored by South Korea's hosting of the Winter Olympic Games, came despite an acceleration in the North's weapons programme previous year and pressure from Seoul's allies in Washington.
While a summit in Pyongyang would signal warming ties on the peninsula, it also risks driving a wedge into the alliance between the US and South Korea.
There were also selfies between North and South Koeran athletes as they waited to walk into the heart of the stadium.
Otto had been in North Korea on an organized tour when he was arrested for allegedly stealing a propaganda poster from a hotel.
But she had no hesitation about attending the Olympics, because she looks around and sees her South Korean neighbors utterly calm.
A DPRK taekwondo demonstration team has also come to demonstrate the traditional Korean martial art during the Winter Olympics . Athletes from North Korea and South Korea marched alongside each other at the 2018 Winter Olympics opening ceremony on Friday.
The unified Korean team marches in the opening ceremony of the Winter Olympics at Pyeongchang Olympic Stadium. Choi and other volunteer helpers at the Games were urged to avoid the topic that another Olympics guest, U.S.
PM @narendramodi had a very cordial meeting with His Majesty King of Jordan immediately upon arrival in Amman . Following the visit, Modi tweeted that "Abu Ammar [Afafat] was one of the greatest world leaders".
Whatever our dreams of exploring the final frontier might be, the economics simply don't make sense when it costs that much. Opinions as to what the object was vary, with some speculating that it was the Falcon Heavy, the most recent SpaceX launch.
The North Korean delegation that arrived in the South on leader Kim Jong Un's private jet also includes his sister Kim Yo Jong . Pence did say, however, that Moon shared with him details of his meeting with North Korean leaders, without elaborating.
Jóhann Jóhannsson , one of the most in-demand score composers in Hollywood, died in Berlin on Friday at the age of 48. The composer also maintained a career as a solo musician; and his latest album, Orphee , was released in 2016.
Ameritas Inv Partners Inc reported 0% in Glu Mobile Inc. (NASDAQ:GLUU). 1.25 million were accumulated by Deutsche Bank & Trust Ag. Staying on top of longer-term price action may help provide investors with a wider range of reference when doing stock analysis.
Moon has invited Kim and other senior North Korean officials to a luncheon at Seoul's presidential palace on Saturday. Friday's ceremony will be attended by North Korea's delegation, including its nominal head of state, Kim Yong Nam.
Across the border the event was taken as a victory, with dozens of Lebanese celebrating and waving Hezbollah's flag. The remains of a missile that landed in the southern Lebanese village of Kaoukaba on February 10.
Tesla initially planned on doing a coast-to-coast autonomous drive in the United States by the end of 2017 but that didn't happen. According to the revised data ... it will take the Tesla about 18.8 months to complete one trip around the sun.
Israeli F-16 jet crashes after Syrian fire
Air raid sirens had gone off in Israel in the early hours of the morning following the UAV interception and raids. That prompted Israel to unleash a dozen retaliatory strikes on both Syrian and Iranian targets inside Syria.
Newcastle United vs Manchester United preview
Newcastle boast the worst home record in the Premier League this season, winning just three of their 13 games at St. Rafa Benitez did well last season to take Newcastle back in the Premier League from the Championship League.
What we learned vs. Atlanta Hawks
Altman had to let James know the front office understood the roster problems - and wanted his input as they set out to fix it.4. Lebron will likely leave Cleveland at the end of the season and the lack of players the Cavs had yesterday was laughable.
Mark Lawrenson states his prediction for Tottenham v Arsenal
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Winter Olympics: Five Olympic gold medals up for grabs
North Korea's nominal head of state Kim Yong Nam also partook in the luncheon with Moon, CBS News' Jacqueline Alemany reports. The United States also has stepped up pressure by stressing human rights allegations against the North Korean regime.
Falcon Heavy changes the game
The Falcon Heavy is the most powerful rocket now operating in the world . One of Musk's key takeaways from the Falcon Heavy's successful flight?
Snow piles up in Midwest storm; traffic snarled
The last part of the area to clear Friday evening according to WGN looks to be Chicago south and east into northwest Indiana. The snow that began falling late Thursday afternoon was expected to continue through Friday as the storm moves east.