Pence also left open the possibility of meeting with North Korea's delegation.
Before leaving Japan for Korea, Pence announced that the US would unveil in coming days "the toughest and most aggressive round of economic sanctions on North Korea ever".
"We haven't requested a meeting with North Korea, but if I have any contact with them - in any context - over the next two days, my message will be the same as it was here today: North Korea needs to once and for all abandon its nuclear and ballistic missile ambitions", Pence said. Whatever sanctions are planned, however, those who value American independence and sovereignty will hope that they are implemented unilaterally, and not by means of the United Nations or one of its affiliated agencies.
Speaking on the conditional of anonymity to describe private conversations, the officials said Moon and Pence agreed that the goal of any opening with North Korea must be denuclearization - even if there are differences in how they'd like to get there.
Yo Jung, who is part of an official delegation that includes the ceremonial head of state, Kim Yong-nam, is expected to arrive to South Korea ahead of the 2018 Winter Olympics in Pyeongchang.
Pence met with President Moon Jae-in to advocate a clear-eyed approach toward his bellicose, nuclear-armed neighbor, warning against North Korean "propaganda" around the games. In addition to showing support for our US athletes, the Vice President will show his confidence in and appreciation for our USA military stationed in the region. North Korea held a parade highlighted by intercontinental ballistic missiles one day before South Korea hosts the opening ceremony of the Winter Olympics.
(The U.S.is said to have an "old" Olympic team with an average age of 27.) Kim Jong-il, father of both Kim Jong-un and Kim Yo-Jon, held the highest office in North Korea (officially the Democratic People's Republic of Korea, the DPRK) from 1997 until his death in 2011.
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Kim Yo Jong would be the first member of North Korea's ruling family to visit the South since the 1950-53 Korean War.
North Korea has recently designated February 8 as its armed forces' day, sparking concerns that the event may dampen a rare reconciliatory mood created by its participation in the February 9-25 Olympics in the South.
"We have never begged for dialogue with the USA nor in the future, too", the North's KCNA news agency said, citing Jo Yong Sam, a director-general in the North's foreign ministry. "There is no need to do so".
Pence told reporters that part of the goal of his visit was to tell "the truth about North Korea at every stop".
North Korea is under multiple sets of UN Security Council sanctions over its banned nuclear weapons and ballistic missile programmes, which have seen it develop rockets capable of reaching the USA mainland.
It remained unclear whether Kim would be carrying a message from her brother to Moon, who has said he is willing to meet Kim Jong Un if he is reasonably sure that such a meeting would help end the crisis over the North's nuclear weapons.