Kim Yong Nam landed in South Korea on Friday along with leader Kim Jong Un's younger sister, Kim Yo Jong, aboard her brother's private jet. She is also the first member of North Korea's ruling family to visit the South since the Korean War.
The significance of Pence and the North Koreans sitting in the same box was not immediately clear.
Kim Yo Jong and her delegation were greeted by government officials, including Unification Minister Cho Myong-gyon, before boarding a bullet train to Pyeongchang.
North and South Korean athletes marched together at the opening ceremony, following months of negotiations by Seoul, which is seeking to use the Olympics to ease tensions over by Pyongyang's nuclear weapons programme.
U.S. Vice-President Mike Pence is using his appearance at the Winter Olympics to call on the worldwide community to get tougher on North Korea's nuclear program and human rights abuses. She and the rest of the North delegation are to join Moon for a meal on Saturday.
But all eyes are on Yo Jong - a key member of the Kim dynasty that has ruled the impoverished, isolated nation with an iron fist and pervasive personality cult over three generations.
Kim Jong Un himself has not left North Korea or met any head of state since 2011 - the year he became the country's leader after the death of his father.
Tensions have been high on the peninsula since previous year when the North staged its sixth and most powerful nuclear blast and test-fired intercontinental ballistic missiles (ICBMS) capable of reaching the U.S. mainland. That has led some athletes to talk about skipping it for fear of hypothermia.
Shivering athletes are bracing for one of the coldest Winter Olympics yet, with temperatures plunging well below zero, while a debilitating norovirus bug has already infected more than 100 people working at the Games.
At the same time, some South Koreans felt optimistic toward South Korea's decision to march under a unified flag with North Korea, as it aligns with the Olympic spirit of peace, cooperation and unity.
On Thursday, North Korea held a military parade attended by Kim Jong-un.
So while relations between the United States and North Korea might be inching towards its lowest ebb, not so the North and South.
An worldwide investigation concluded it had been torpedoed by a North Korean submarine, a charge Pyongyang denies.
Moon is also scheduled to hold a summit with Japanese Prime Minister Shinzo Abe, during which they are expected to discuss the North Korea standoff and the sensitive issue of "comfort women", a euphemism for girls and women forced to work in Japan's wartime brothels.
Its agents blew up a South Korean airliner ahead of the 1988 Seoul Olympics in an attempt to dissuade visitors; then it boycotted its rival's Olympic debut on the world stage.