The vice president said he "reaffirmed" the United States' commitment to a denuclearized North Korea during a meeting with South Korean President Moon Jae-in.
Kim's sister, Kim Yo Jong, was at the opening ceremony with North Korea's nominal head of state, 90-year-old Kim Yong Nam.
Kim Yo Jong is the first member of the ruling Kim family bearing the bloodline of the sacred Mount Paektu, a centerpiece of the North's idolization and propaganda campaign, to cross the border into the South since the 1950-53 Korean War.
Moon, for his part, took the opportunity to highlight the visit of North Korean officials to the global competition, referring to the "Olympic Games of peace".
Pence also has promised the USA will soon unveil "the toughest and most aggressive round of economic sanctions on North Korea ever".
The vice president says there is no equivalence between the show of American force and the North Korean military parade held Thursday on the eve of the Olympics.
This items corrects that Kim Yo Jong is the leader's sister.
He also did not shake hands with Kim Yong Nam while making a brief appearance at a leaders' reception ahead of the ceremony - although Japanese Prime Minister Shinzo Abe, whose country is also regularly threatened by Pyongyang, did so, while exchanging pleasantries with the North Korean.
Spencer O'Brien finishes 22nd in women's slopestyle
Anderson's gold marks Team USA's second gold medal of PyeongChang 2018 after snowboarder Red Gerard won gold over the weekend. She will compete in big air, scheduled for February 23, which makes its Olympic debut in PyeongChang.
Officials of the South Korean presidential palace say Moon told Kim Yo Jong words of appreciation about her attendance at the opening ceremony until late hours despite the cold temperature. Pence carried a similar message during his trip to Japan and South Korea.
North Korea has made clear that it does not intend to negotiate away its nuclear and missile programs in return for relief from worldwide sanctions.
Dressed in long, white padded jackets, they followed the flag with a blue silhouette of the Korean Peninsula against a white background.
But analysts say it may be more hard for the South to arrange a summit with the North coming off a year in which Pyongyang test-fired dozens of missiles, including three ICBMs, and conducted its most powerful nuclear test to date.
The U.S. -led worldwide community has been tightening the screws on North Korea with sanctions created to punish its economy and rein in its efforts to expand its nuclear weapons and missile program, which now includes developmental long-range missiles targeting the U.S. mainland.
The North-South Olympics detente has raised concerns in Washington and Tokyo that Seoul may ease up on a "maximum pressure" campaign by the United States and its allies to get Pyongyang to abandon its nuclear and missile programmes.
Just before the opening ceremony, Kim Yong Nam attended a dinner for visiting foreign dignitaries hosted by Moon.
In dispatching the highest level of government officials the North has ever sent to the South, Kim Jong Un revealed a sense of urgency to break out of deep diplomatic isolation in the face of toughening sanctions over his nuclear program, analysts say.
The North has sent almost 500 people to the Pyeongchang Games, including officials, athletes, artists and also a 230-member state-trained cheering group after the Koreas agreed to a series of conciliatory gestures for the games.