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The Trump administration's recent allegations and actions against China have "directly impacted our mutual trust and cast a shadow over our bilateral relations", Chinese Foreign Minister Wang Yi told Secretary of State Mike Pompeo Monday, casting the sudden deterioration in the relationship in surprisingly undiplomatic terms.

The top U.S. diplomat met with the North Korean leader in Pyongyang for two hours before Pompeo flew to South Korea on Sunday afternoon for a two-day visit.

State Department spokesperson Heather Nauert said in a statement that "Chairman Kim invited inspectors to visit the Punggye Ri nuclear test site to confirm that it has been irreversibly dismantled".

The US is pushing for a "final, fully verified denuclearisation" but North Korean Foreign Minister Ri Yong-ho told the United Nations general assembly in September there was "no way" his country would disarm first as long as tough US sanctions remained against his country. Without this access, intelligence agencies and other experts have had to rely on satellite images and scattered reports from sources inside the country in order to gauge whether or not there has actually been any progress. Mr Trump cancelled Mr Pompeo's planned trip to Pyongyang in August, citing little evidence that North Korea had followed through on any of its commitments to denuclearise.

Secretary of State Michael Pompeo told South Korean President Moon Jae-in upon his arrival in Seoul that Kim had agreed to meet with Trump "as soon as possible", according to a statement from Moon's office.

Trump met with Kim in Singapore in June and - at the time - announced that the two countries are set to "start a new history".

During the meeting in Beijing, Wang said China and the U.S. should strengthen cooperation on North Korea.

"Most importantly, both the leaders believe there's real progress that can be made, substantive progress that can be made at the next summit", Pompeo said.

After spending about five hours in Beijing, Pompeo headed for the airport to return to Washington.

The Sunday stop in Pyongyang was Pompeo's first chance to introduce his special envoy for North Korea, Stephen Biegun, to leaders there.

Pompeo identified Punggye-ri as one of the testing sites mentioned in their conversations.

Pompeo's visit to Pyongyang marked the fourth of its kind.

Since Trump and Kim met, US-North Korea relations have stalled.

On a more positive note, Wang said China was still willing to solve the trade dispute with the USA through negotiations, "but they must be conducted on an equal, honest and serious basis".

The two diplomats had warmer words regarding efforts to curb North Korea's nuclear ambitions.

"Recently, as the US 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 interests, and has made groundless criticism of China's domestic and foreign policies", Wang said at a joint appearance with Pompeo.

Moon also said there was a possibility of Kim holding a summit with Japanese prime minister Shinzo Abe.