The game, played before South Korean President Moon Jae-in and North Korean leader Kim Jong Un's younger sister, was the first played by a Korean hockey team at the Olympics.
Moon apparently cited the conditions necessary for an inter-Korean summit.
The South Korean president also stressed the need for the communist North to resume its dialogue with the United States.
Trump, who has at times exchanged taunts and threats with Kim, said in early January after the first intra-Korean talks in over two years that the United States was willing to speak to North Korea "under the right circumstances", although it was far from clear whether this would pay dividends.
Tensions between the two soared previous year as Pyongyang tested missiles capable of reaching the US mainland and its most powerful nuclear device to date, while Kim Jong Un and US President Donald Trump traded personal insults and threats of war. The South Koreans want to use the Olympics to ease tensions spurred by North Korea's pursuit of nuclear weapons. Asia experts said Pence's sour conduct toward the North Koreans could be seen as disrespectful to the South Korean hosts, who were demonstrating a moment of harmony with the North.
The North's official Korean Central News Agency also referred to Moon as president.
Leaders of the two Koreas have only meet twice since the peninsula was divided in 1948.
The invitation was delivered to Moon when the North's delegation paid a visit to him on Saturday.
There was U.S. vice president Mike Pence's warning that even though he was attending the opening ceremony, he wasn't going to enjoy himself (or something like that).
Pence, who is leading the USA delegation to the Olympics, briefly encountered Kim Yong-nam at the Games but the two tried to avoid directly facing each other.
She told CBS the North Korean athletes would be trailed by chaperones, making defection virtually impossible.
But it made no mention of US President Mike Pence, who was seated in the same box as Moon and the two North Koreans.
The vice president's visit was also marked by bad blood between Pence and some US athletes.
But he rejected any suggestion Sunday that even a temporary warming of relations between the North and South could drive a wedge between Seoul and Washington.
"Although many Koreans are welcoming North Korea's participation in the Pyeongchang Winter Olympics, there are also significant criticism and concerns both domestically and internationally", the statement said.