During the most recent summit between Korean leaders in September, Kim told Moon that he would "greatly welcome" the Pope to Pyongyang, according to South Korea's presidential office. It came amid expectations that his meeting with leader Kim could provide momentum to get the denuclearization process going again after a monthslong stalemate over how to rid the North of its nuclear weapons program.
The President said that a second summit "is happening" and that the "timing won't be too far away".
Pompeo's retort came after Wang accused the United States of escalating trade disputes, interfering on Taiwan and meddling in the country's domestic affairs.
Wang, also a state councillor, accused Washington of escalating the trade conflict, interfering with Taiwan, and levelling false accusations about China's domestic and foreign policies, according to a readout posted on China's foreign ministry website.
While Kim's actions since have fallen short of Washington's demands, the Trump administration is preparing for a second summit.
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Before Kim Jong Un's grandfather, Kim Il Sung, established the North Korean regime, Pyongyang had more Christians than any other city on the peninsula and was widely known as the "Korean Jerusalem".
The North Korean leader told President Moon of his intention when the two men met for a summit last month.
In a statement, State Department spokeswoman Heather Nauert said Kim had invited inspectors to visit the Punggye-Ri test site in order to confirm that it had been dismantled.
The visit was Pompeo's fourth to North Korea.
The trade war between China and the USA is however being seen as a barrier to co-operation in the North Korean crisis.
"While the U.S. side has constantly escalated trade frictions with China, it has also taken actions regarding Taiwan that harm China's core interests", Wang said. Pompeo was in Tokyo for talks with Japanese officials ahead of his trip to North Korea. We continue to make progress on agreements made at Singapore Summit.
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When Pope Francis visited South Korea in 2014, he held a special mass in Seoul dedicated to the reunification of the two Koreas.
There's no sign that North Korea is slowing down its production of nuclear fuel.
"These actions have damaged our mutual trust, cast a shadow over China-US relations and are completely out of line with the interests of our two peoples", Wang told his US counterpart.
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.
The Beijing stop could be tense as it comes days after Vice President Mike Pence delivered a blistering speech accusing China of military aggression, commercial theft, rising human rights violations and electoral intervention against Trump.
Trump said "eventually we're going to have lots of meetings on U.S. soil and on their soil by the way".
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