Though Moon has used the Olympics to resurrect meaningful communication with North Korea after a diplomatic stalemate over its nuclear program, he didn't immediately jump on the North Korean offer for a summit.
Many observers agreed the North had won this round in the propaganda battle, but many hurdles lie ahead before a lasting solution is reached.
A spokesperson for President Moon said he hoped the two countries would work towards a summit and called on the United States and North Korea to resume dialogue.
Kim Yo-jong carried a bright blue folder as she entered the conference room at the Blue House, Seoul's presidential office, and some analysts speculated it could contain a letter from her brother.
The message was delivered by Kim's sister, Kim Yo-jong, during a meeting with Moon at Cheong Wa Dae.
Tensions on the Korean border have escalated over the past year as the North pursues its ambition of becoming a fully-fledged nuclear power.
Pence kept up the pressure in the days ahead of the Olympics, frequently denouncing the North's record of human rights abuses to counter what he called Pyongyang's "propaganda charade".
South Korea may also need to persuade traditional allies the United States and Japan, which have raised concerns that the North is attempting to use its outreach as a release valve for worldwide pressure.
White House officials and other critics believe North Korea is trying to use the global stage to gain sympathy and ease punishing economic sanctions and diplomatic pressure that are beginning to bite.
Pence, who left South Korea on Saturday, told reporters traveling with him that Moon had informed him about the meeting with North Korean officials.
"The vice president is grateful that President Moon reaffirmed his strong commitment to the global maximum pressure campaign and for his support for continued sanctions", Pence spokeswoman Alyssa Farah said when asked about the developments.
Moon and Pence didn't discuss an invitation extended by Kim Jong Un to meet with the South Korean leader in Pyongyang, said a senior White House official who requested anonymity to discuss internal deliberations.
"You must have had a hard time due to the cold weather", Moon said as he greeted Kim Yo-jong, referring to the frigid temperatures during Friday's opening ceremony.
The two Koreas are still technically at war after the 1950-53 conflict on the Korean peninsula ended in a ceasefire and not a truce.
The Koreas previously held summits in 2000 and 2007, both hosted in Pyongyang by Kim Jong Il, Kim Jong Un's late father.
North Korea has said it will never give up its nuclear deterrent and critics in the South see its participation in the Games as a reward for bad behaviour.
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