The invitation came during talks and a lunch Moon hosted with Kim Yo Jong, the younger sister of the North Korean leader, at the presidential Blue House in Seoul.
South Korean President Moon Jae-in has been using the Games in his efforts to break the ice with the North and pave the way for talks over the North's weapons programme.
However, South Korea has been more willing to re-engage with the North than its old USA war ally, which wants Seoul to keep piling diplomatic and economic pressure on its neighbor.
Pence's comments suggested that the administration of President Donald Trump, which has mostly taken a hard line over any potential engagement with North Korea, might be looking more favorably at diplomatic options.
It would be the first summit in more than a decade between Korean leaders. Kim Yo Jong is 28 years old, according to the USA government.
Seohyun's talent and popularity is just one reason she was likely chosen for the performance: also has expressed her interest in politics in the past, citing former UN Secretary-General Ban Ki Moon as her inspiration; Seohyun met Ban in 2012, when he was serving as a Goodwill Ambassador.
Those are the flags of united Korea that athletes from North Korea and South Korea marched under during Friday's Opening Ceremony.
"I wanted to show that there are many people who support North Korea, who support a single South-North team", said Lee Eun-ha, a college student among the pro-unification crowd. The previous meetings came after rounds of global talks aimed at eliminating the North's nuclear program, which eventually failed.
The 30 year-old, an increasingly prominent figure in her older brother's government, was the North's first ruling family to visit the South since the end of the Korean War. The Koreas could potentially talk about a South Korean special envoy meeting Kim Jong Un in Pyongyang or even a summit between Moon and Kim.
The luncheon also includes Choe Hwi, chairman of the North's National Sports Guidance Committee, and Ri Son Gwon, chairman of the agency that deals with inter-Korean affairs. In January 1968, Kim Yo Jong's grandfather, founding North Korean president Kim Il Sung, sent a squad of North Korean commandos to Seoul who tried unsuccessfully to kill then-president Park Chung-hee.
Accepting North Korea's demand to transport more than 100 members of the art troupe by sea, South Korea treated the Mangyongbong-9 ferry as an exemption to the maritime sanctions it imposed on the North.