Cheong Wa Dae (South Korean presidential office) spokesperson Kim Eui-kyeom said that Yo-jong came to South Korea as a "special envoy of Kim Jong-un".
Pence said Friday that the USA would oppose talks between the two Koreas until the North agreed to open negotiations on ending its nuclear program.
The South Korean president also stressed the need for the communist North to resume its dialogue with the United States.
The North sent the delegation to attend the opening ceremony of Pyeongchang Olympics on Friday, during which the two nations' athletes marched under a unified flag.
But North Korea's awful record on human rights and the growing threat from its nuclear weapons program appeared out of mind. Some have speculated that it could contain a message from the North Korean dictator.
The four senior DPRK delegates will have a meeting and lunch with President Moon on Saturday, according to South Korea's presidential Blue House.
The two Koreas are technically still at war after a conflict in the 1950s ended with an armistice, rather than a peace treaty.
At the opening ceremony of the Olympics on Friday night, Moon and Kim Yo Jong shook hands in what appeared to be a friendly manner.
"Working in unity on the way to unification", Kim Yong-nam wrote.
Moon sought to reassure U.S. Vice President Mike Pence that the allies remained in lockstep despite North Korea's joint appearance at the Olympics.
In an interview with NBC's Nightly News, Pence spoke about taking action against any upcoming nuclear threats posed by North Korean.
The invitation was delivered to Moon when the North's delegation paid a visit to him on Saturday.
While a summit in Pyongyang would signal warming ties on the peninsula, it also risks driving a wedge in the alliance between the US and South Korea.
Meanwhile, Fred Warmbier, father of Otto Warmbier, an American student who died aged 22 after being detained in North Korea for a petty offence previous year, was not in the box with Pence but rather sitting with the United States athletes, according to The Washington Post Tokyo bureau chief Anna Fifield.
The North Korean delegation is set to return home Sunday.