Past "charm offensives" have been interpreted as North Korea trying to recoup from crippling sanctions on their nuclear programme, or trying to drive a wedge between Seoul and its U.S. ally.
South Korea's principal opposition party, the Liberty Korea Party, was not impressed.
For its part, Japan has made clear that it favors the swift resumption of joint US-South Korean military exercises, which had been put off until after the Olympics in an effort to smooth the path for North Korea's participation at PyeongChang.
To pave the way for the North's participation at Pyeongchang, South Korea had delayed the annual exercises with US forces, which usually take place between February and March, until after the Olympics.
"Now is not the time to postpone U.S. It is important to move forward with the drills as planned", Japanese Prime Minister's Shinzo Abe told Moon in what appeared to be an awkward encounter, the Blue House said. "North Korea is skilfully driving a wedge between the U.S., Japan and South Korea".
North Korea's race to build an intercontinental ballistic missile that could hit the United States with a nuclear warhead has raised fears of a devastating conflict.
The missive was delivered by Kim's visiting sister Kim Yo-jong, who said he was willing to meet "at the earliest date possible", a spokesman for South Korea's presidential palace said.
North Korea heads for diplomacy gold medal at Olympics
Her presence helped the theme of Korean unity to dominate the opening ceremony as the two Koreas marched under one flag. The U.S will not allow the propaganda charade by the North Korean regime to go unchallenged on the world stage.
"No pressure comes off until they are actually doing something that the alliance believes represents a meaningful step toward denuclearization", Pence was quoted as saying.
"We should firmly keep in mind that any talks where denuclearisation is not a precondition only to buy North Korea more time to complete its nuclear capabilities while they fool us with their peace offensive facade", said Chang Je-won, a party spokesman said, according to Reuters.
Mr Moon is eager to use Kim Yo Jong's presence at the games to restore regular communication with North Korea and eventually pull it into nuclear talks.
After the threats, missile launches and general nastiness from the North over the previous year, there is still a lot of anger, fear and scepticism in the South.
What did seem clear was that, deliberately or not, the North Korean government had managed to edge its way onto center stage during the South's biggest global moment in years. Later in the day, Moon and the North's delegation also jointly attended the opening match of the unified women's ice hockey team comprising athletes from the two Koreas.
One notable visual came with the appearance of the Russian delegation, which marched in unable to carry its flag because of doping-related sanctions by the International Olympic Committee.