If Seoul does decide to send a special envoy to the North, local analysts say the presidential Chief of Staff Im Jong-seok, Unification Minister Cho Myoung-gyon or National Intelligence Service (NIS) Director Suh Hoon - all of whom accompanied Moon when he received the North Korean delegation at the Blue House last Saturday - are possible options.
A unified Korean women's ice hockey team, first of its kind in the Olympic history, has won the hearts of millions on Saturday night, despite a 8-0 loss to the Sochi bronze victor Switzerland in their debut at the PyeongChang Olympic Games.
The North Korean delegation's visit to South Korea was the first trip since August 2009, when a high-level North Korean delegation attended the funeral of former South Korean President Kim Dae-jung, who held the first-ever inter-Korean summit with then North Korean leader late Kim Jong-il in 2000.
The meetings between North and South continue Saturday when President Moon holds a luncheon with the North Korean delegation.
A senior United States government official says that Moon urged Pence to meet with the North Korean delegation, but Pence left the Olympic venue without doing so.
Ms Kim, believed to be 30, is the first in the ruling Kim family to set foot in South Korea since the two countries were separated by the 1950-53 Korean War.
Syria condemns 'US massacre' after strikes kill 100 pro-regime fighters
And while the USA -led coalition mission hasn't changed and ISIS is on the run, work remains to be done, she said. Russian officials assured the Coalition they would not engage coalition forces in the vicinity.
A renewed feud over the issue has frayed ties even as America's two key Asian allies confront the challenge of North Korea's nuclear and missile programmes.
"All options are on the table and the United States has deployed some of our most advanced military assets to Japan and the wider region to protect our homeland and our allies and we will continue to", vowed Pence. Later, he skipped a formal dinner at which he was due to share a table with North Korea's ceremonial head of state Kim Yong Nam.
Although Kim Yo Jong ranks diplomatically lower than Kim Yong Nam, as Kim Jong Un's sister she is considered more important in North Korea. Kim Jong Il's sushi chef, Kenji Fujimoto, nicknamed them North Korea's "Prince" and "Princess" due to their upbringing and closeness to the former North Korean leader.
The Japanese Prime Minister visited South Korea for the opening ceremony of the 23rd Winter Olympics at the country's east county of PyeongChang.
It was the US that appeared to be the one left in the cold, especially after the sister of the North Korean dictator extended an invitation from her brother for Moon to visit the North.
Kim Jong-un's invitation to Moon raises prospects for the first inter-Korean summit in more than 10 years.
Up the road, however, an elderly husband and wife, each draped in the South Korean flag, denounced Moon as a "fake president".