"There is no daylight between the United States, the Republic of Korea and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear and ballistic missile program", Pence told reporters during the return flight to the United States.
Moon responded to the invitation by suggesting the two countries "should accomplish this by creating the right conditions", adding that talks between North Korea and the United States were also needed, and requested that North Korea be more active in talking with the U.S., according to the spokesman.
According to South Korean media, this is the first time in more than eight years that North Korean senior officials visited the Blue House - since August 2009, when the North's delegates paid respects at the funeral of former president Kim Dae-jung.
Visiting US Vice President Mike Pence did not engage with the North Korean representatives just a few seats away at the opening ceremony, and did not get up to cheer when athletes from the host nation and its neighbour entered the arena together behind a unification flag.
Short track is one of the most popular sports in South Korea and as a series of home skaters reached the later rounds of the men's 1,500 meters and the women's 500, the North Koreans celebrated by waving flags in support.
But there seems to be a diplomatic thawing between North and South Korea.
Lee is also set to meet with Kim Yo-jong, the sister of North Korea's leader Kim Jong-un, the next day after she and other members of the North Korean delegation were received by South Korean President Moon Jae-in.
Tensions between the two soared past year as Pyongyang launched intercontinental ballistic missiles capable of reaching the USA mainland and carried out by far its most powerful nuclear test to date.
Kim Yo Jong offered an invitation from her brother for Moon to visit the North, in the strongest sign yet of an expanding diplomatic opening opposed by the U.S.
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If an inter-Korean summit is held, it will mark the third of its kind and first under the Kim Jong-un regime.
Kim Yong Nam, the North's ceremonial president, said "even unexpected difficulties and ordeals could be surely overcome and the future of reunification brought earlier when having a firm will and taking courage and determination to usher in a new heyday of inter-Korean relations". His son Otto was jailed in North Korea and died upon his return to the U.S. past year after suffering extensive brain damage. President Moon welcomed Kim Yo-jong and another high-ranking North Korean official for lunch at the presidential residence, and she took the opportunity to extend an official invitation for Moon to visit North Korea.
Neither did Pence 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 did so.
Although South Korea has been a trenchant supporter of Trump's campaign of "maximum pressure" against North Korea, Moon has been keen to use the Olympics to pry open the door to better relations with its adversary.
"The president (of the IOC, Thomas Bach, ) nearly as a bridge sat between the president of the Republic of Korea and the honorary head of state of the DPRK last night and they were talking throughout the hockey", Adams said, using the abbreviation for North Korea's official name, the Democratic People's Republic of Korea.
As the women's 500-meter qualifying heats began, USA vice president Mike Pence was settled in at the Gangneung Ice Arena with his wife and president Moo Jae-in. Moon's office initially provided conflicting accounts of whether he accepted the invitation, with a Blue House spokesperson later clarifying that pre-conditions first needed to be met.
North Korea is sending 22 athletes, including the Alpine skiers, to Pyeongchang thanks to special entries given by the International Olympic Committee amid rare reconciliation mood between the rival Koreas.
North Korea's Alpine skiing coach says it's an "honor" to compete at the Pyeongchang Olympics, though he doesn't expect much from any of his three athletes.