Moon responded to the invitation by suggesting the two countries "should accomplish this by creating the right conditions", adding that talks between North Korea and the United States were also needed, and requested that North Korea be more active in talking with the USA, according to Kim Eui-kyeom.
"On a political level in Seoul, there is no wedge that can be driven between us by North Korea", Mattis said, echoing comments made by U.S. Vice President Mike Pence. South Korea's presidential Blue House also had no immediate comment.
Pence said Friday that the US would oppose talks between the two Koreas until the North agreed to open negotiations on ending its nuclear program.
"This is the strongest action yet by North Korea to drive a wedge between the South and the United States", said Kim Sung-han, a former South Korean vice foreign minister and now a professor at Korea University in Seoul.
"It was a good symbol of hopefully what the Olympic Games and the Olympic spirit can do", IOC spokesman Mark Adams said of Saturday's hockey game.
The two Koreas remain technically at war after their 1950-53 conflict ended in a truce rather than a peace treaty.
The Olympics-inspired detente mood flared after North Korean leader Kim Jong Un abruptly expressed his willingness to send an Olympic delegation. "That is a very unusual time, if in fact he is trying to show a warming", Mattis said, referring to Kim Jong Un.
Moon was invited to a summit with Kim, even as the United States warned against falling for Pyongyang's Olympic charm offensive.
Last night, both Moon and Kim attended the first official Olympic match by the unified Korean women ice hockey team, which they lost 8-0 to the Swiss team.
Speaking at the ceremony, ROK President Moon Jae-in called the Games a "festival and celebration of peace".
Short-track speed skating makes its Pyeongchang debut with South Korea's best hope for a haul of gold medals, Choi Min-jeong, starting her campaign for a 500m qualifiers.
"Let's not whitewash North Korea's record".
But Mr Moon, a liberal who has always wanted to engage the North, will also have to convince a good portion of his own people who are deeply wary about North Korean intentions.