But unlike his last visit to Beijing in June, Pompeo did not have a meeting with Chinese President Xi Jinping.
"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.
The restrictions for Pompeo's recent talks with North Korean leader Kim Jong-un were voiced by his "old" diplomatic partner, Kim Yong-chol, a former North Korean spy chief who has been negotiating with the U.S. on nuclear issues. "But we do think right that this is a place where ultimately some of these big hard issues have to be resolved by the nation's most senior leaders and hope to have those presented in a way that the two leaders can resolve them when they get together".
The possibility of a summit between Kim and Japanese Prime Minister Shinzo Abe is also "open", Moon said, adding: "A new order is being created on the Korean peninsula".
"After having a nice meeting we can enjoy a meal together", Kim told Mr Pompeo as they walked down a hallway toward a guesthouse dining room. He said those actions have affected trust between the US and China and that the United States should stop "this kind of mistaken action".
"We have to see whether North Korea will let inspectors sample the soil at the Punggye-ri site for detailed analysis, or simply confirm that the site explosion was real".
Pompeo did not have a scheduled meeting with Chinese President Xi Jinping, a fact that a senior U.S. State Department official on the trip said was not odd, even though top U.S. officials often meet Chinese heads of state on visits.
Ballon d'Or 2018: Ronaldo, Courtois nominated but De Gea misses out
Liverpool's Brazilian goalkeeper Alisson Becker, Frenchman Karim Benzema and Edinson Cavani completes the five-man list. Premier League duo Roberto Firmino and Eden Hazard are among the nominees for the 2018 Ballon d'Or .
The statement said the two leaders "discussed the upcoming second summit between President Trump and Chairman Kim and refined options for the location and date of that next summit".
Meeting at the Diaoyutai Guest House, Wang told Pompeo that the U.S. had "stepped up rhetoric over trade tensions" after a raft of tit-for-tat tariffs on billions of dollars of United States and Chinese goods. Korean Central News Agency (KCNA) reported that Kim had "warmly welcomed" Pompeo in Pyongyang and "spoke highly of him".
Moon said a second Mr. Trump-Kim summit could be accompanied by major diplomatic developments that could contribute to the denuclearization of the Korean Peninsula and stabilizing peace.
Pompeo's trip was the latest turn in a diplomatic saga that saw Trump and Kim threaten each other with nuclear war a year ago only to sign a vague agreement in June to "work toward complete denuclearization of the Korean Peninsula".
Specifically, Pompeo revealed that North Korea agreed to allow global inspectors to survey their nuclear and missile testing sites. US officials have thus far said the penalties will remain in place until the North's denuclearization is fully verified.
Washington and Pyongyang have sparred over the exact terms of the vaguely-worded agreement in Singapore, with the U.S. pushing to maintain sanctions and pressure against the North until its "final, fully verified denuclearisation".
"I would certainly expect so", the official said.