Meanwhile, Kim Eui-kyum, the spokesman of the South Korean President, while announcing the official visit of Moon to Pope Francis, specified that the president will also carry a message from North Korean leader Kim Jong-un to the Pope.
"A new order is being created on the Korean Peninsula", Moon declared.
The Vatican had no immediate comment on the North Korean leader's invite.
That makes any focus on a second Trump-Kim summit misguided, Klingner of Heritage said. But that wasn't an advance on comments Trump made last month in NY, when he said he wanted to meet Kim "very soon".
In May, Pyongyang failed to follow through with its promises to allow inspectors to assess its demolition of Punggye-ri in what has become a roadblock in the country's denuclearization commitment.
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.
He also expressed gratitude towards Trump for making a honest effort to implement the agreements that were made in their previous summit in June.
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".
Kim told Moon of his wish to meet the pope during last month's summit of the two leaders, the spokesperson added.
The Pontiff has said he wants to visit Japan next year.
In a summit in April, the leaders of South and North Korea agreed to cooperate in declaring an end to the war this year, saying that they will seek multilateral talks involving the USA and possibly China.
"Recently, as the USA side has been constantly escalating trade friction toward China, it has also adopted a series of actions on the Taiwan issue that harm China's rights, and has made groundless criticism of China's domestic and foreign policies", Wang said at the joint appearance with Pompeo. "We made significant progress".
Pompeo retorted that "the issues that you characterised, we have a fundamental disagreement". Catholic priests are prohibited in North Korea.
Given the delicate nature of talks with North Korea, it's possible that Pompeo and his hosts reached agreements not yet made public.
While the Chinese Ministry of Foreign Affairs told a news conference that broader tensions would not undermine cooperation on North Korea, Wang told Pompeo that the issue illustrated the importance of maintaining a working relationship.
"These actions have damaged our mutual trust, cast a shadow over the future of China-US relations, and go against the interests of the people of the two countries", Wang told Pompeo. While tensions flared in the region, bringing the U.S. and North Korea to the brink of military confrontation, the pontiff warned that a "widespread war" would destroy "a good part of humanity". A second summit in the coming weeks could boost Trump ahead of US midterm elections in November, but a failure to secure any measurable commitments would undercut what the president has seen so far as a clear foreign policy strength.
Pompeo said they came close to finalising a date and venue for the next Kim-Trump meeting.