Abe said he had confirmed with Moon the need to maintain strong pressure on North Korea to get it to abandon its nuclear and missile programmes, reiterating Tokyo's stance that "talk for the sake of talk is pointless".
The team took to the ice for the first time on Saturday, losing to Switzerland but winning over the crowd as North Korean cheerleaders and South Korean fans roared the players on.
The offer could put Moon in a delicate diplomatic quandary, but he avoided a direct response, said his spokesman Kim Eui-kyeom, and called instead for efforts to "create the right conditions" for a visit.
The official also noted that while Trump believes in talking, in this case, the issue is not about words but about deeds on North Korea's part.
Pence spent the days leading up to the Pyeongchang Olympics warning that the North was trying to "hijack the message and imagery" of the event with its "propaganda".
But as tensions rose between the North and Washington, the Games triggered a rapid reconciliation between the two Koreas, who are still technically at war.
"We're getting along great", the Kim Jong-un lookalike told Reuters.
North Korea agreed to participate in PyeongChang after Games' host South Korea and the International Olympic Committee encouraged the reclusive, heavily-sanctioned state to participate as a gesture of peace. If peace is not imminent, a summit in Pyongyang between Mr Moon and Kim Jong Un seems better to most than the threats of recent months. The senior U.S. official said Pence was not trying to avoid the North Korean officials but rather ignore them.
Moon shook Kim's hand; Pence stared forward and refused to engage with her.
"With my bro up from north woo hoo let's go!"
Speaking past year at his swearing-in ceremony, Moon said he would be willing to travel to Pyongyang "under the right conditions", adding that "for peace on the Korean Peninsula, I will do everything that I can do".
It was the first time an inter-Korean team had competed at an Olympic Games.
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