Seoul's presidential office says Moon during the luncheon proposed a toast calling for peace and "mutual prosperity" for the two Koreas.
North Korean media slammed Pence what they described as "snobbish" behavior.
Internet problems before and during the opening ceremony of the Winter Olympics on Friday night are being investigated as a possible cyberattack, officials said Saturday. Lawmakers from Moon's liberal ruling party have talked about the possibility of South Korea sending a special envoy to Pyongyang to meet with Kim Jong-un.
However, no member of North Korea's ruling family has ever before visited the Blue House, which is near where North Korea founder Kim Il Sung - Kim Yo Jong's grandfather - sent dozens of commandos to assassinate former South Korean military strongman Park Chung-hee in 1968.
"There is no daylight between the United States, the Republic of Korea and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear and ballistic missile program", Mr Pence told reporters on a flight back to the US from South Korea.
The website was only normalized on Saturday morning even as the details of where the attack originated remain unknown, the organizers said.
Neither approach inspired a goal from the home team, which went down 0-8, but it was clear who connected with the mainly young South Korean fans, who have grown up physically separated from the poor, one-party state to the North. He'd been dispatched from Washington for the Olympics in part, he said, to make sure the world didn't forget that North Korea was a misbehaving and risky neighbor in the community of nations.
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The athletes elicited a standing ovation by most leaders in the VIP box, including Moon and Kim's sister.
"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. Even if he had met the North Korean officials, Pence would simply have reiterated his mantra that North Korea can not reap the benefits of being part of the community of nations while it threatens the world with its nuclear and missile aggression.
Following his stint with the American delegation at speedskating, Moon attended a hockey game with Kim Yong Nam - the nominal North Korean head of state - on Saturday night.
The offer could put Moon in a delicate diplomatic quandary, but he avoided a direct response, said his spokesman Kim Eui-kyeom, and called instead for efforts to "create the right conditions" for a visit. A large delegation from North Korea, dressed in identical garb and cheering in careful coordination, watched from an upper deck of the stadium.
The invitation, reports Reuters, was delivered by Kim Yo Jong, and has been "practically" accepted by Moon.
Already there have been concerns that North Korea's overture of the sports diplomacy is an indirect attempt by the regime to wedge a rift between the US and South Korea.