The North Korean invitation puts Moon in a hard position as he seeks a rapprochement with the north on the one hand and a desire not to upset the USA on the other.
Kim's unusual invitation, which was received by Moon with both caution and optimism, was the latest sign of growing closeness between the two rival governments after an exceptionally tense period over the North's nuclear weapons program.
Seoul's Unification Ministry said Friday that the Mangyongbong-92 will return to the North on Saturday.
The smiles and handshakes at the meeting were friendlier than some of the North's past history with the complex - in 1968 it sent commandos to attack it to try to assassinate the South's then leader.
The hermit kingdom has been slapped with round after round of sanctions, aimed at strangling its resources and forcing the regime to reign in its nuclear and ballistic missile programmes.
As the crowd in the viciously cold stadium erupted in joy to celebrate the march of the athletes with their country's flag swinging in the cold wind, the unified march of South Korea and North Korea turned the stadium into a cauldron of noise.
The spokesman said Moon and the high-ranking DPRK delegation made a broad range of discussions on inter-Korean relations and issues on the Korean Peninsula "under a friendly atmosphere".
Two Turkish pilots die in Syria crash
Also Sunday, at least three civilians were killed in government airstrikes and shelling on a besieged, opposition-held area outside Damascus, according to the Observatory.
Murray and the players have simple but lofty goals for a team ranked 22nd in the world a year ago: Win a game in the three-game preliminary round; advance out of pool play; and help hockey grow in South Korea.
Moon and Kim Yo Jong will have another opportunity to talk when they attend the second and final performance by a visiting North Korean orchestra on Sunday evening in Seoul, a Blue House official said. It figured to be because no matter which side of the border they were representing, Korean hockey players simply aren't ready to compete on such a big world stage.
Tensions soared previous year as the North staged a series of nuclear and missile tests in violation of United Nations resolutions, while leader Kim and United States President Donald Trump traded colorful insults and threats of war.
Switzerland's Alina Muller nearly single-handedly spoiled Korea's Olympic unity moment on Saturday, scoring four goals to power the Swiss to an 8-0 win over Korea's unified women's ice hockey team.
Moon said improved relations between the Koreas may be a step toward resolving the nuclear standoff.
"What can not be overlooked is that Moon did not directly demand North Korea to abandon its nuclear development".
The Kim sister put her hands to her mouth early in the match when North Korean forward Jong Su Hyon went close.
South Korea's president held landmark talks with the North's ceremonial head of state and the sister of its leader Kim Jong Un today, even as the USA warned against falling for Pyongyang's Olympic charm offensive. However, he did not meet with Yong-nam and Yo-jong.
The younger Kim's trip to the South marks the first time that a member of the North's ruling dynasty has visited since the Korean war, which ended in an armistice in 1953. Later, he skipped a formal dinner at which he was due to share a table with North Korea's ceremonial head of state Kim Yong Nam.