Spectators were visibly moved, HuffPost Korea reported, with some in the audience tearing up at the sight. "He & I both reaffirmed our commitment to the denuclearization of the Korean Peninsula".
The U.S. leader vowed before and during his trip to South Korea that he would not let the North use the Olympics as a propaganda tool to cover up its human rights abuses.
The games already have became a diplomatic feat as much as an athletic one.
Earlier in the day, Moon met the North Korean delegation at the South Korean presidential office, Cheong Wa Dae (Blue House).
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Prior to the opening ceremony on Friday night, Pence arrived late to a dinner reception between the two Koreas and greeted everyone at a main table except for Kim Yong Nam, North Korea's nominal head of state, Reuters reports.
The handwritten invitation to President Moon was delivered by Mr Kim's influential sister, Kim Yo-jong, at a landmark meeting in the presidential palace in Seoul, as the Games opened on Saturday.
Pence spoke at a memorial in Seoul that was prepared to remember 46 South Korean sailors after their ship was sunk in 2010.
"South Korea has some hard homework to solve regarding some countries", Mr Moon said before Mr Pence arrived. "The vice president will remind the world that anything the North Koreans do during the Olympics is a charade to disguise the reality of the oppression inside North Korea".
After what appeared to be a grueling climb to the top of the stairs, they handed the flame to Olympic gold and silver medal-winning figure skater Yuna Kim, who still stood well out of reach of the cauldron.