The meeting will be held from 11 a.m.at Seoul's presidential office Cheong Wa Dae, followed by lunch hosted by Moon, according to Cheong Wa Dae spokesman Kim Eui-kyeom.
The meeting comes one day after Moon and the North Korean officials attended the opening of the Winter Olympic Games in PyeongChang located some 180 kilometers east of Seoul.
Earlier, at a VIP reception before the ceremony, Pence went around a table and shook hands with all the dignitaries except Kim Yong Nam, North Korea's 90-year-old nominal head of state.
The figures from the two Koreas shared kimchi (Korean pickled cabbage) and soju rice liquor, and spoke for three hours.
U.S. President Donald Trump and the North Korean leadership traded insults as tensions rose, with Trump repeatedly dismissing the prospect or value of talks with North Korea.
"I am very confident, as President Trump is, that President Moon will continue to stand strongly with us in our extreme-pressure campaign", Pence told NBC in an interview on Friday, maintaining all options were open to deal with the crisis.
Speaking on Thursday, Pence said: "Allow me to assure you and the people of South Korea that the U.S. will continue to stand shoulder-to-shoulder in maximum pressure until North Korea finally and permanently and irreversibly abandons nuclear and ballistic ambitions".
"Make no mistake about it, the United States of America has viable military options to deal with a nuclear threat from North Korea but, that being said, we hope for a better path", he said.
Other members of the North Korean delegation present at Saturday's meeting included Ri Son Gwon - who led the first sit-down talks at the Demilitarized Zone (DMZ) earlier this year, and Choe Hwi.
This came after he promised the USA will announce the "toughest and most aggressive round of economic sanctions on North Korea ever".
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. 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.