He didn't say what those conditions were, but he urged North Korea to open a dialogue with the United States, suggesting no diplomatic progress could be made without USA participation.
Instead, Pence was criticized by North Korean media, accused of not respecting the "Olympic spirit". Her presence is the latest move in an extraordinary show of Olympic diplomacy with Seoul that could prove to be a major challenge to the Trump administration's hard-line Korea policies.
CNN's favorable description of Kim, who shares both parents with North Korea's leader and is one of his closest confidants, was in contrast to the remarks by South Koreans the network interviewed.
Despite Pence's hardline stance and words, he has also signaled the United States is possibly open to negotiations when he said in regards to the North Korean officials, "I haven't requested any meeting".
Turns out the North Korean leader is actually an Australian named Howard.
Precautions need to be taken against a situation in which a rift would emerge in global efforts to contain North Korea, while there is no progress being made on the North Korean nuclear issue.
Shortly after North Korea invited the South Korean leader, Pence's office issued a statement.
Pyon said he was happy to see the Korean hockey team competing with a "single-minded" unity, saying the two Koreas could also field a joint Alpine team in the future.
At Friday's opening ceremony, for example, Moon shook hands with Jong, as Pence, sitting merely feet away, looked stone faced, never acknowledging the North Korean delegation.
The nuclear-armed dictator was identified by The Telegraph as an Australian musician named Howard, while his spray-tanned companion was played by American Dennis Alan.
The United States insisted it would continue its policy of exerting global pressure on North Korea in an effort to get it to abandon its nuclear program.
In Rome on Sunday, US Defence Secretary Jim Mattis said it was too early to tell whether reduced tension between the two Koreas would last beyond the Olympics but that "on a political level in Seoul, there is no wedge that can be driven between us by North Korea".
President Trump's right-hand man was at the Gangneung Ice Arena on Saturday night to watch the opening session of short-track speedskating and, for the second evening in succession, he was unable to avoid a connection to North Korea.
The invitation came during talks and a lunch Moon hosted with Kim at the presidential Blue House in Seoul.
Moon should make efforts to hold fast to the US-South Korean alliance.