"I know that during your visit, you also want to exchange views with the Chinese side on regional hotspot issues including the situation in the Korean Peninsula", Wang said. Trump hinted of more progress during a news conference in NY last month, and Pompeo said Monday that he would only discuss details the two sides had agreed to release.
"We require that the U.S. stop such misguided actions", he said, adding that the two countries should pursue cooperation "and not descend into conflict and confrontation".
The polite but edgy tone underscored the plunge in US-Chinese relations as the administration of President Donald Trump confronts Beijing over its technology policies and territorial claims in the South China Sea.
He further added that strategic US-China dialogue was something China chose not to undertake.
Trump and Kim held an historic first summit in Singapore in June.
Since the denuclearisation effort got underway with a secret visit to the North by then-CIA chief Pompeo in April, there has been only limited progress, even since the 12 June Trump-Kim summit that many had hoped would jump-start the effort.
In late 2015, top North Korea official Kim Yang Gon reportedly died in a auto accident.
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Kim also brought up the interactions between the North Korean leader and Roman Catholic Archbishop Hyginus Kim Hee-joong at Mt. Paektu last month, who was invited to join the South Korean delegation alongside President Moon.
High-level exchanges between the two countries have been frozen, including a planned diplomatic and security meeting between US Secretary of Defence James Mattis and Chinese defence minister Wei Fenghe originally scheduled for mid-October in Beijing.
While China's foreign ministry said at a news briefing Monday that broader tensions wouldn't undermine cooperation on North Korea, Wang told Pompeo that the issue illustrated the importance of maintaining a working relationship.
Nuclear diplomacy later stalled because of suspicions over how honest North Korea is about its disarmament pledge.
The trade war between China and the United States is however being seen as a barrier to co-operation in the North Korean crisis.
In July 2017, North Korea television aired footage of a traffic park, including go-carts or mini-vehicles, being driven by North Korean children.
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". "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".
The U.S. Pacific Fleet is drafting plans for a global show of force to warn China and demonstrate resolve to deter Beijing's military actions, CNN reported Thursday, citing several unidentified U.S. defense officials.