President Donald Trump's administration has taken a hard line on North Korea's nuclear and ballistic missile program, saying there is no room for negotiations unless Pyongyang abandons it.
The two Koreas remain technically at war after their 1950-53 conflict ended in a truce rather than a peace treaty.
Trump, who has at times exchanged taunts and threats with Kim, said in early January after the first intra-Korean talks in over two years that the United States was willing to speak to North Korea "under the right circumstances", although it was far from clear whether this would pay dividends.
After the game, the top North Korean officials and the South Korean president joined Bach in greeting the Korean players and posing for pictures with them. Jo Yong Sam, department director general of North Korea's foreign ministry, said Thursday the country had never "begged the USA for dialogue" and wasn't about to start now.
After the invitation was conveyed, a Blue House official said local authorities are now planning what message Moon will send to Kim Jong-un, and how he will send it, once the PyeongChang Winter Olympic Games wrap up later this month. US Vice-President Mike Pence, sitting a few seats away in the same Opening Ceremony VIP booth, looked stony faced as the scene unfolded.
South and North Koreans marched together under a unified flag at the games' opening ceremony.
During his meeting with the four defectors, including some who had been tortured and abused by the North, Pence warned that the world would see "a charm offensive by North Korea" Friday.
"We will not allow North Korea to hide behind the Olympic banner the reality that they enslave their people and threaten the wider region", he said.
Mr Moon could find himself in a delicate diplomatic position in the North Korean bid.
Still, Cho is known to be trusted by Moon when it comes to dealing with the North, and the cabinet member has the most experience in inter-Korean dialogue within the Unification Ministry.
USA officials have been urging South Korea to be cautious in its rapprochement with the North.
He said war had forged "the core of the bond" between the USA and South Korea and that helps explains "why there is no daylight and there will be no daylight" between the two.
North Korea's cheer squad opted for perfectly synchronised moves, songs from home and catchy slogans such as "Unify the motherland!".
Addressing tens of thousands of troops and civilians assembled on the square below him, Kim said the parade marks North Korea's emergence as a "global military power" despite facing the "worst sanctions".