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Pope Francis has never been to North Korea and only visited the southern part of the peninsula once, in 2014.

"China and United States relations are at an important juncture and facing challenges", Yang said.

Kim Jong Un wants Pope Francis to visit his country and believes he would be welcomed "enthusiastically", according to South Korean officials.

"President Moon had said the Pyongyang summit must receive the support of the worldwide community, and suggested [inviting the pope] would be one way" of earning trust, a South Korean presidential Blue House source told Hankyoreh.

"On the issues that you characterized, we have fundamental disagreements..."

The two sides agreed to set up "working-level" negotiating teams to finalize the date and time for a summit, as well as set the stage for a successful summit meeting, he said.

South Korean President Moon Jae-in will deliver Kim's invitation when he meets Francis next week during his trip to Europe, Blue House spokesman Kim Eui-kyeom told a news briefing.

Those disagreements - a burgeoning trade war, China's territorial claims in the South China Sea and us policy toward Taiwan - are unlikely to be resolved any time soon.

Denuclearisation of North Korea is "a long process", Pompeo said, adding: "We made significant progress". In June, NBC News reported that an updated intelligence assessment concluded that North Korea was stepping up production of fuel for nuclear weapons at secret sites across the country.

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Pompeo said it is important for the two allies to have a "fully coordinated, unified view of how to proceed, which will be what is needed if we are going to be successful on denuclearizing North Korea".

Stephen Biegun, new US nuclear envoy who was accompanying the secretary, said he offered on Sunday to meet his counterpart, Vice Foreign Minister Choe Son Hui, "as soon as possible" and they were in discussion over specific dates and location.

Trump has insisted the global community must stick to the sanctions against North Korea until Kim denuclearises.

Moon said a second Trump-Kim summit could be accompanied by major diplomatic developments that could contribute to the denuclearization of the Korean Peninsula and stabilizing peace. Trump said on Twitter that, "Progress made on Singapore Summit Agreements!"

Later Kim said, "It's a very nice day that promises a good future" for both countries.

The North has accused Washington of making "unilateral and gangster-like" demands on denuclearization and has insisted that sanctions should be lifted before any progress in nuclear talks.

The inspectors will be allowed in as soon as the two sides agree on "logistics", Pompeo told reporters in Seoul before leaving for Beijing on a whirlwind diplomatic trip.

The Vatican had no immediate comment on the North Korean leader's invite.