A 2014 survey by Korea Gallup showed 22 percent of South Koreans identify themselves as Buddhist, while almost 30 percent are Christian. The visit was the latest indication of deteriorating ties between the USA and China, as the two sides tussle over everything from trade to Taiwan and the South China Sea.
"President Moon had said the Pyongyang summit must receive the support of the global community, and suggested [inviting the pope] would be one way" of earning trust, a South Korean presidential Blue House source told Hankyoreh.
Pompeo said there are many issues on which Washington and Beijing disagree but it is important that both sides listen to each other.
Pompeo said there was agreement that Kim and President Donald Trump would hold their second summit as soon as possible, but plans for a sequel to their June meeting in Singapore already were in the works.
Kim also brought up the interactions between the North Korean leader and Roman Catholic Archbishop Hyginus Kim Hee-joong at Mt. Paektu last month, who was invited to join the South Korean delegation alongside President Moon.
Pompeo also visited Japan and South Korea, where he said Monday in Seoul that there had been "significant progress" toward an agreement for the North to give up its nuclear weapons.
The secretary of state's previous trip to North Korea, in July, did not go so well.
North Korea's reported overture comes a few weeks after the Vatican signed a landmark deal with Communist China, North Korea's closest ally, over bishop nominations, aimed at ending decades of tensions that contributed to dividing the Chinese church and hampered efforts at improving relations between China and the Vatican.
"We're setting that up right now", Trump told reporters Tuesday in the Oval Office.
Trump has insisted the worldwide community must stick to the sanctions against North Korea until Kim denuclearises. He flew back to the USA with little new to show for three days of lightning diplomacy.
The Secretary of State did not meet Kim on that trip.
Trump said "eventually we're going to have lots of meetings on United States soil and on their soil by the way".
He came away from it saying the two sides had made progress, only for North Korea to denounce him for making "gangster-like" demands and raising "cancerous" issues.
The KCNA said that Kim also expressed "will" and "conviction" to make progress on issues of mutual concern, apparently indicating the denuclearization talks that have nearly been stalled since the June summit in Singapore. He also urged world leaders to mediate in the crisis and find a diplomatic solution.