In an unusually public rebuke, Chinese Foreign Minister Wang Yi accused the USA of undermining mutual trust between the countries as Pompeo sat across from him.
Recently the United States escalated its trade friction with China, took actions that jeopardized China's rights and interests on the Taiwan issue and unwarrantedly condemned China on its domestic and foreign policies, Wang said.
Since Donald Trump and Kim Jong-un met in Singapore in June, US-North Korea relations have stalled.
At least, a US official traveling with Pompeo said, the visit to North Korea went better than Pompeo's previous trip, which ended with a North Korean statement accusing him of making "gangster-like" demands.
He said North Korean leader Kim Jong-un had agreed to allow global inspectors into the Punggye-ri nuclear test site that was dismantled in May.
Moon also said the North will "permanently dismantle" its missile engine testing site and launch platform in the northwestern town of Tongchang-ri in the presence of experts from "concerned countries".
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Last month, the North's foreign minister told the United Nations there was "no way" his country would disarm first as long as tough U.S. sanctions remain against his country.
Denuclearisation of North Korea is "a long process", Pompeo said, adding: "We made significant progress".
Meeting at the Diaoyutai Guest House, Wang told Pompeo that the United States has "stepped up rhetoric over trade tensions" after a raft of tit-for-tat tariffs on billion of dollars in USA and Chinese goods.
Mr Moon has said he expects Mr Kim to visit Russian Federation soon and possibly meet with Japanese Prime Minister Shinzo Abe, although he has not commented on the likelihood of the Pope travelling to Pyongyang.
"During the meeting with Pope Francis, [Moon] will relay the message from Chairman Kim Jong-un that he would "greatly welcome" the Pope if he visits Pyongyang", Moon's spokesman, Kim Eui-kyeom, told reporters.
The Vatican said in a statement that the pope will receive Mr Moon at midday on October 17.
Weakening support for US -led sanctions - from countries including Russian Federation and China, but also South Korea - has also led to a growing sense that Pompeo is spending more and more of his time just trying to keep existing restrictions in place.
"There's a lot of logistics that will be required to execute that", Pompeo told a news briefing in Seoul before leaving for Beijing.
China and Russia - North Korea's traditional allies - called for relaxed sanctions against Pyongyang at the UN Security Council last month, saying "steps. toward gradual disarmament should be followed by an easing of sanctions".
South Korean Foreign Minister Kang Kyung-wha has given a hint of what a grand bargain between the two countries could look like.
The secretary of state's previous trip to North Korea, in July, did not go so well. While tensions flared in the region, bringing the United States and North Korea to the brink of military confrontation, the pontiff warned that a "widespread war" would destroy "a good part of humanity".
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