Mr Moon said the Koreas should "make it happen" and encouraged the north to return to negotiations with the US.
The proposal was announced in a meeting between North Korean leader Kim Jong-un's sister, Kim Yo-jong.
The response was seen as meaning that there should first be progress on efforts to resolve the North Korean nuclear standoff, such as talks between the United Sates and the North, before what would be a third inter-Korean summit takes place. But it would be Kim's first meeting with a foreign head of state.More news: Jerusalem was highlight of my year, says Donald Trump
Cyber security experts had warned of potential attacks on the Winter Olympics, with both North Korea and Russian Federation touted as possible sources.
Earlier Friday, Pence went to even greater lengths to avoid Kim Yong-nam at a dinner put on by South Korean president Moon Jae-in. The supporters waved blue and white flags that showed an undivided Korean Peninsula.
But one of the women told reporters they had traveled from North Korea's capital, Pyongyang.
The pair were greeted at the airport by South Korean Unification Minister Cho Myong Gyon. Others fear it is an omen of larger political ambitions of the North.
And then, during the ceremonies, as North and South Korean athletes entered the stadium together under a unified flag, Pence and his wife Karen remained seated while everyone around them rose to applaud.
Kim Yo Jong has rapidly risen up the ladder since her brother inherited power from their father, and is now among his closest confidantes.More news: Amid Olympic Détente, Pence Snubs North Koreans In Visit To Pyeongchang
A North-South Olympics detente has raised concerns in Washington and Tokyo that Seoul may ease up on the "maximum pressure" campaign by the United States and its allies to rein in North Korea.
Pyongyang conducted its largest nuclear test a year ago and in November tested its most advanced intercontinental ballistic missile that experts said has the range to reach anywhere in the United States.
But both sides have held their ground.
The women arrived in South Korea in charter buses on Wednesday.
If "diplomatic dance" were an event at the Winter Olympics, Kim Jong Un's younger sister would be favored to win gold.
As if to drive the point home, Kim Jong-un used the eve of the Olympics to throw a massive military parade in Pyongyang that was highlighted by several huge intercontinental ballistic missiles rolled out in launcher trucks. "With his summit proposal, he seeks to incite friction between Seoul and Washington by widening their policy gap".More news: Uncle charged with murder after death of niece, 11
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