North Korea has sent some of the highest level officials ever to the south for these games, the result of diplomacy by Seoul that led to an agreement between the two countries - still formally at war - to participate together in the Winter Games.
Kim Yo Jong has also captured the media's attention.
North Korea, meanwhile, has shown no signs of abandoning its nuclear and missile programs, maintaining its hostile posture toward Washington. Moon had said "let's create conditions to make it happen", the official said, an indication that Moon was likely to accept the invitation.
"It is absolutely necessary for the North and the United States to engage in talks at an early date", he cited Moon as saying.
Hundreds of Twitter users in recent days have referred to "Pyongyang2018", and while some were making a dig at the presence of North Korea at the Games, in many cases it appears to have been a simple mix-up.
President Trump has traded insults with North Korea's leader and has led efforts to slap sanctions on the country for its refusal to yield to global pressure to halt its nuclear weapons program.
"He [Pence] could have sat with the US delegation and avoided the box but he chose not to. knowing the North Koreans would be seated behind him", said a USA official.
"President Moon and President Trump are completely aligned in their objective for a nuclear-free Korean Peninsula", U.S. Vice President Mike Pence also said Friday in South Korea. But he and his wife did greet everyone at the top table - all except Kim Yong Nam, North Korea's nominal head of state.
After departing South Korea this week, she said there was a shared excitement with many people. "No one else in leadership can bring messages directly to Kim Jong Un".
There is worry too that the proposed summit Pyongyang may come with preconditions - a North Korean speciality. In a statement, organizers issued an apology "to all those affected". Kim Yo Jong's promotion previous year brought her closer to the center of power in the isolated state.
"She is a bit of a mystery figure", Madden said.
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.