Analysts say the North's Olympic diplomatic drive seeks to loosen international sanctions against it and undermine the alliance between Seoul and Washington.
Pence, speaking to reporters aboard Air Force Two after attending the opening ceremony of the Games in Pyeongchang, South Korea, said that he and President Moon Jae-in "continue to stand strong" and coordinate efforts against the North.
"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 said as he flew back to the United States.
Global alarm at the rapid advance of nuclear-armed North Korea's weapons technology rose further last year when the regime tested its Hwasong-15 ballistic missile theoretically capable of hitting the mainland US, in a challenge to Washington that has threatened to "utterly destroy" the regime in the event of an attack.
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President Donald Trump and the North's leader Kim Jong Un have engaged in a series of personal insults.
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.
The invitation was issued through Kim's sister, Kim Yo Jong, who was attending the Games with the North's ceremonial head of state Kim Yong Nam.
Pence did not interact with the North Koreans even though he was seated in the same box as them at Friday's opening ceremony.
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.
Moon did not respond directly to the invitation from Kim Jong Un, and urged Pyongyang to actively seek an "absolutely necessary" dialogue with Washington, Moon's spokesman said.
A senior US administration official told reporters that Pence did not discuss North Korea's invitation to Moon when the two leaders watched short track speed skating together.
Although inter-Korean talks are occurring on the sidelines of the Olympics, Pence is confident that Seoul and Tokyo "are solidly with our alliance and the need to continue and intensify economic sanctions," the official said.