Another planned trip by Pompeo to Pyongyang was scrapped after what Trump said was insufficient progress towards implementing the terms of the Singapore declaration.
Pompeo's retort came after Wang accused the U.S. of escalating trade disputes, interfering on Taiwan and meddling in the country's domestic affairs.
Wang said U.S. actions have damaged China's rights and interests, undermined mutual trust and cast a shadow over China-U.S. relations.
North Korea's official name is the Democratic People's Republic of Korea or DPRK.
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".More news: Modric v Ronaldo rematch as Ballon d'Or nominees unveiled
Pompeo told journalists in Seoul that the leader had agreed to open up the Punggye-ri nuclear testing site to inspectors. Washington and Beijing "should and must make the correct choices", Yang said.
US officials have thus far said the penalties will remain in place until the North's denuclearization is fully verified.
Pompeo said they came close to finalising a date and venue for the next Kim-Trump meeting.
"It's a long process", Pompeo told reporters Monday. "We've made incredible progress - beyond incredible".
Pope Francis has also this year expressed support for ongoing improving inter-Korean relations, saying the April 27 Panmunjom summit represented "a concrete route toward reconciliation and regained brotherhood with the aim of guaranteeing peace on the Korean Peninsula and in the entire world".
There are doubts whether Kim is willing to fully relinquish his country's nuclear weapons, which he may see as a stronger guarantee of survival than whatever security assurances the United States could provide.More news: Brett Kavanaugh Confirmed, Possibly Most Conservative Supreme Court Since 1934
Wang's remarks made clear that China is most concerned about United States moves to improve ties with Taiwan.
Moreover, Chinese officials signaled the discord undermines efforts to cooperate on North Korea, making the US bid to disarm Kim's regime even less likely.
Kremlin spokesman Dmitry Peskov said Russian Federation had invited Kim to visit, but the time and place had yet to be agreed. Japan has been wary of the initiative, but South Korea has embraced it.
It comes nearly two decades after a similar invitation was extended to Pope John Paul II, although a visit never came to pass after a request for Catholic priests to be accepted in North Korea was denied.
In an interview with the Washington Post, she said the North could agree to dismantle Yongbyon, its signature nuclear site.
The North's regime since then has allowed Catholic organisations to run aid projects in the impoverished country, but direct relations with the Vatican are non-existent.More news: Bucking party, Murkowski charts her own path on Kavanaugh