Before they turned the page on decades of public acrimony, the leaders regularly traded threats and insults as North Korea pushed to develop a nuclear missile capable of hitting the United States. Trump also approved a weapons sale to Taiwan, the self-ruled island the Communist mainland claims as its own territory, and sanctioned a Chinese company and its leader over an arms purchase from Russian Federation.
Although freedom of religion is protected under North Korea's constitution, in practice worship is tightly controlled and limited to state-run institutions.
Pompeo said he was also hopeful that Kim would allow inspectors to visit a "missile engine test site", believed to be a facility in the town of Tongchang-ri that North Korea says it has begun dismantling.
North Korea maintains a Catholic church in Pyongyang, the Jangchung Catholic Church, though it is not affiliated with the Holy See.
In their later meeting, Yang expressed Chinese frustration with Washington while avoiding specifics, telling Pompeo relations are "facing challenges".
"We hope the United States and China can meet each other halfway and conscientiously fulfill the important consensus reached by the leaders of both countries", Yang said.
Pompeo said the two sides agreed to have "more frequent and higher-level working group discussions than we've had in some time on a set of issues" and stressed that "ultimately some of these big, hard issues have to be resolved by the nations' most senior leaders, and we're hoping to have those presented in a way that the two leaders can resolve them when they get together".
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Both he and another man are wanted for attempted murder for a Novichok attack on Sergei Skripal and his daughter Yulia in March. Dawn Sturgess , 44, died in June after being exposed to the same weapons-grade nerve agent after it was apparently discarded.
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 Pope has long urged the two Koreas to make peace.
Pompeo met with the North Korean leader in Pyongyang on Sunday to rekindle stalled denuclearisation talks following a landmark summit between Kim and US President Donald Trump in Singapore.
"There was an exchange of stands of the top leaderships of the two countries on the issues arising in holding the second DPRK-US summit talks to be followed by an in-depth discussion of them", the KCNA said. But immediately after the news, the Vatican press office released a statement confirming that the pope would receive South Korea's president in an audience at the Vatican on October 18.
A similar situation occurred in June 2000 after then-President Kim Dae-jung returned from his summit with North Korean leader Kim Jong Il in Pyongyang, telling the press he would convey an invitation to visit Pyongyang to Pope John Paul II.
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.