After delivering an invitation for Moon to visit Pyongyang earlier on Saturday, Kim arrived dressed in a black fur-collared coat and took her seat next to North Korea's ceremonial head of state Kim Yong Nam, with Olympic chief Thomas Bach also present.
North Korea's state media also sharply criticized Pence.
"The grievances that the world has about North Korea are very legitimate".
Many experts say Kim's overture is meant to use improved ties with Seoul as a way to weaken USA -led global sanctions toughened after its series of big weapons tests a year ago that include its sixth and largest nuclear test explosion and three intercontinental ballistic missile launches.
South Korea's then president Kim Dae-jung, who won a Nobel Peace Prize for his Sunshine policy of engagement with the North, visited Pyongyang for an unprecedented inter-Korean summit with late leader Kim Jong Il.
Turkish soldiers killed, 11 injured in Afrin
The United States said Syrian pro-government forces initiated an attack on the US-backed Syrian Democratic Forces (SDF). Turkish officials say the leaders of Turkey, Russia and Iran will meet in Istanbul to discuss peace efforts for Syria.
Washington is not expected to support the initiative - recently the Trump administration has been exerting "maximum pressure" on North Korea to abandon its nuclear programme.
In Rome on Sunday, U.S. Defense Secretary Jim Mattis said it was too early to tell whether reduced tensions between the two Koreas would last beyond the Olympics but that "on a political level in Seoul, there is no wedge that can be driven between us by North Korea".
Pence, speaking to reporters aboard Air Force Two after attending the opening ceremony of the Games in Pyeongchang, South Korea, said that he and President Moon Jae-in "continue to stand strong" and coordinate efforts against the North.
While Moon did not hesitate to shake hands and smile with his North Korean visitors, Pence didn't appear to even look in the direction of the North Korean delegation during the Friday event.
Before leaving South Korea on Saturday evening, Pence watched short track speed skating games, with Fred Warmbier seated behind him.
Kim Yo-Jong invites South Korea's Moon to North Korea
She is reportedly the first member of Jong-Un's family to travel South across the border since the Korean War. A Moon-Kim summit would mark the first time leaders of two countries have met in 11 years.
South Korea's figure skating superstar and Olympic gold medalist Kim Yuna lit the Olympic cauldron. Not only did he get South Korea to breach its own direct sanctions by allowing a North Korean ferry to bring musicians to the South for the Olympics, but he also persuaded the United Nations to suspend global sanctions, even if only for three days.
The first medals of the Pyeongchang Olympics will be awarded Saturday, but most attention will be focused on a preliminary round hockey match featuring the combined Korean women's hockey team.
There was early criticism in South Korea that the new players would throw off team chemistry and cost South players time on the ice after working together for months to shine on the sport's biggest stage.
"I know that people are watching for a wedge between South Korea and the United States".
Kim Jong Un Invites South Korean President Moon Jae-in To Pyongyang
It has only deepened over the years as the North closes in on the ability to field an arsenal of nukes that can hit USA cities. Pence and the North Korean delegation, who both attended the Games opening ceremony, had no contact with each other.
U.S. Vice President Mike Pence is also in Pyeongchang for the opening ceremony. The athletes' blue and white uniforms represent the Korean unification flag.