Mr Kim held an unprecedented summit with US President Donald Trump in Singapore in June, and pledged to work toward denuclearisation of the Korean peninsula.
Pope Francis is already set to meet with South Korean President Moon Jae-in October 18 for an audience at the Vatican Apostolic Palace, where Moon will personally deliver the invitation from Kim Jong Un.
On a more positive note, Wang said China was still willing to solve the trade dispute with the United States through negotiations, "but they must be conducted on an equal, honest and serious basis".
Pompeo said on Monday the two sides were "pretty close" to agreeing on details for a second summit.
Pompeo's trip to Asia began Saturday in Tokyo, where he met with Prime Minister Shinzo Abe.
This version of the story corrects 4th paragraph to make clear that Washington has been seeking inspection of Yongbyon.
The Catholic Church, like any other religion, is only allowed to operate in North Korea under extremely tight restrictions, and within the confines of the KCA.
North K0rea's definition of nuclear disarmament to this date has included an insistence that the US also disarm.
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Pompeo told reporters Kim had said he was ready to allow global inspectors into North Korea's Punggye-ri nuclear testing site and the Sohae missile engine test facility as soon as the two sides agreed on logistics.
"You have no nuclear tests, you have no rockets, and we have a very good relationship with Chairman Kim, which is very important", Trump said.
Following his arrival in Seoul from Pyongyang on Sunday, Pompeo said at a meeting with South Korean President Moon Jae-in that he had "a good productive conversation" with Kim, in talks which represented "another step forward".
The U.S. and Japan have pushed for the North to compile and turn over a detailed list of its nuclear sites to be dismantled as a next step in the process. "At the same time, China also resolutely protects its sovereignty, security and development interest", he said.
Time reported that the invitation to Pope Francis is not the first time North Korea has offered to host a papal visit.
That progress contradicts promises North Korea has made dating back at least to 1992, and in recent months, when Kim promised to honor all past agreements and work toward denuclearization.
The President said that a second summit "is happening" and that the "timing won't be too far away".
KCNA said "there was an agreement on the issue of holding the working negotiation for the second DPRK-U.S. summit talks as early as possible, and relevant procedure-related issues and ways were also discussed".
But Kim Il Sung, the North's late founding leader and the current ruler's grandfather, viewed Christianity as a threat to his authoritarian rule and eradicated it through executions and labor camps.