Moon told Pence the USA and South Korea had "airtight" cooperation and hoped the Olympics could lead to denuclearization of the peninsula. "But it also needed do tone down its rhetoric and actions as a peace initiative toward South Korea during the Olympics".
But critics in the South say Seoul has made too many concessions to Pyongyang, and demonstrators protested on Thursday as a North Korean orchestra gave a sold-out performance in Gangneung, which is hosting Olympic events.
Hinting at more engagement with Pyongyang, Seoul said it would be open to discussing resuming tours to North Korea's Mount Kumgang once the security of tourists was guaranteed and conditions relating to North Korea's nuclear programme were met.
South Korean tours to the Mt Kumgang resort were closed after a South Korean tourist was shot by a North Korean guard there in 2008. They will stay for just three days.
An employee at Samsung Electronics' booth in PyeongChang, South Korea, last week. His noncommittal attitude has prompted speculation, but hopes that such an encounter would come to fruition quickly thinned Thursday as Pyongyang announced it has no plans to meet USA officials. The South hosts 28,500 USA troops, a legacy of the war.
North Korean state television broadcast footage of the parade a few hours after it concluded.
Referred to as Kim Jong-un's "army of beauties", the cheering squad is expected to root for its own national athletes, and possibly the South Korean national team.
Seoul is set Friday to welcome North Korean leader Kim Jong-un's sister Kim Yo-jong along with senior official Choe Hwi, who are blacklisted under American and United Nations sanctions, respectively.
By sending a relative, "Kim Jong Un may be trying to present himself as an equal to Donald Trump", Hong said.
While the main organiser of the Olympics said the display would not affect the "dynamics" of the event, the United States had said it would prefer the North did not go ahead with it.
While at face value, Kim Yo Jong's appearance at the Games might seem like a sign of good will, it is also a distraction from the actual event and a deterrent to what has taken place between North Korea and other countries in the past year leading up to this point.
But his comments did not rule out a meeting - and nor has Pence.
Making his way to Pyeongchang to lead the US delegation to Friday's opening ceremonies, Pence has embarked on a set of symbolic visits created to draw attention to the North's awful human rights record and nuclear aggression.
North Korean leader Kim Jong Un watched on as tanks and thousands of troops staged a military parade on Thursday, marking seven decades since the formation of the country's armed forces.
"It looks like North Korea had potential reaction from the global community in mind and toned down the scale and message of the event a lot", said Lim Eul-Chul, a North Korean studies professor at Kyungnam University.
Japanese Prime Minister Shinzo Abe meets with Moon on Friday. Pyongyang had initially announced plans to send one during the 2014 Asian Games in Incheon, but scrapped the plans weeks before the games.