It warned against agreeing to talks before North Korea scrapped its nuclear program, saying it would only "benefit the enemy".
"But today we thought it was important to make sure the truth is told".
South Korean athletes who have represented the country in different sports carried the flag around the stadium and then the traditional guard of honor raised the flag. Pence and Japanese Prime Minister Shinzo Abe declined to appear in a photo with the rest of the officials present, including the North Koreans.
Korean defenseman Marissa Brandt, who was adopted by an American couple and raised in the United States, said the integration of the North Koreans had not been disruptive.
A private jet took off from Incheon airport in South Korea, carrying Kim Yo Jong, the younger sister of North Korean leader Kim Jong Un, and the rest of the North's unprecedented deputation whose presence drew the spotlight away from sporting endeavor and raised uncomfortable questions for South Korea's allies. It has dispatched a delegation of almost 500 people - mostly musicians, dancers, and an all-female cheering squad - and has been pushing its participation as a sign of willingness to work with Seoul, through greater exchanges, to ease what has been a year of very high tensions on the peninsula. During the trip, Pence has kept up pressure on the north over its nuclear ambitions and human rights record.
North Korea has sent some of the highest level officials ever to the south for these games, the result of diplomacy by Seoul that led to an agreement between the two countries - still formally at war - to participate together in the Winter Games.
South Korea, which is using the Pyeongchang Games to break the ice with North Korea, seated its presidential couple alongside U.S. Vice President Mike Pence and his wife, with two of the North's most senior officials sitting in the row behind.
"North Korea must recognize that the strong ties between Japan, the United States and South Korea will never waver", he told reporters after meeting with Moon.
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The statement from the Ministry of Unification came after the North Korean delegation concluded its three-day visit. The visit included an invitation for South Korean President Moon Jae-in to travel to Pyongyang for talks.
But South Korea's presidential Blue House said Pence had a meeting scheduled with United States athletes and had only planned to stay briefly to greet other officials.
On Friday night, a huge crowd gathered in the freezing Olympics Stadium as performances displayed the sweep of Korean history and culture. He repeatedly called Kim Jong Un's regime "the most tyrannical" on Earth and studiously avoided talking to or even acknowledging the North Korean delegation, even when they sat just feet apart in the VIP box at the opening ceremony.
After a chaotic year of nuclear war threats and nuclear and missile tests from the North, it was an evening of striking visual moments. But speculation is growing it might fire off another if South Korea and the United States resume joint military drills after the Paralympics in March.
But the pinnacle of Pence's messaging was at the opening ceremony itself, where his personal guest was the father of American student Otto Warmbier, who died past year after being returned home in a coma after his 17-month detention in North Korea.
Japan and South Korea have been at odds since the Moon administration announced in January internal findings on how the comfort women pact was reached before its signing under the administration of his impeached predecessor, Park Geun-hye.
The downside for Washington is that it could expose growing differences with Seoul on the best way to deal with North Korea and achieve the ultimate goal of denuclearization.
In part, Moon said that to completely resolve the issue, there was a need for Japan to offer a honest apology to the former comfort women.