Tensions are rising: US and Chinese destroyers had a near-miss in the South China Sea recently near Gaven Reef, part of the disputed Spratly archipelago where China has developed military outposts.
Kim told Moon of his wish to meet the pope during last month's summit of the two leaders, the spokesperson added.
As Pyongyang continues to take big diplomatic strides, analysts say the United States may soon be pushed into a corner to relax sanctions.
Kim held an unprecedented summit with US President Donald Trump in Singapore in June, and pledged to work toward denuclearisation of the Korean peninsula.
Speaking at the conservative Hudson Institute, Pence accused China of using trade, diplomatic overtures and military expansion to spread its influence, and he called on American business leaders, academic scholars and journalists to counter Beijing's campaign.
Pompeo spent around 3.5 hours with Kim in Pyongyang on Sunday, in a formal meeting and then at lunch, talks he later described as "productive" and "another step forward" in negotiations to convince North Korea to give up its nuclear weapons program.
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Deputy Superintendent Fiore did not comment on speed, or whether the occupants of the vehicle had been wearing seat belts. They said they would be open on Sunday and will being collecting donations for local volunteer emergency services.
Pompeo also invoked the cancellation of a meeting between US Defense Secretary Jim Mattis and his Chinese counterpart, which was supposed to take place this month in Beijing. "We demand that the USA side stop this kind of mistaken action".
The inspectors will visit a missile engine test facility and the Punggye-ri nuclear testing site as soon as the logistics are worked out, Pompeo said.
The Vatican's priests were expelled by North Korea long ago and state-appointed laymen officiate services.
Pompeo also met China's top diplomat Yang Jiechi, a Politburo member who heads the ruling Communist Party's foreign affairs commission, though remarks before reporters took a more conventional tone, even as both agreed relations faced many challenges.
"President Trump is very close to losing control", he said.
The desire to welcome the leader of the Catholic church comes as Kim attempts to transform his image from paranoid head of a rogue state to young and dynamic world leader.
But, as Pompeo made his way back to Washington after three days of talks in Tokyo, Pyongyang, Seoul and Beijing, it was unclear what had been accomplished. "But if you look at the approach, we are in lockstep with each of those two countries in terms of how we approach achieving the results that everyone is aimed at".
The Vatican did not comment on the possibility of a papal visit.