U.S. Secretary of State Mike Pompeo, right, is greeted by U.S. Ambassador to South Korea Harry Harris upon his arrival at Osan Air Base in Pyeongtaek, in South Korea, Sunday, Oct. 7, 2018, after his North Korea trip. Korean Central News Agency (KCNA) reported that Kim had "warmly welcomed" Pompeo in Pyongyang and "spoke highly of him".
Kim expressed enthusiasm for the future of talks between the two nations.
Responding to Wang's remarks, Pompeo said he wanted to come to Beijing to "have discussions".
"We require that the U.S. stop such misguided actions", he pointed out, adding that the two countries should pursue cooperation "and not descend into conflict and confrontation".
Pompeo replied that it was "important that we listen to each other, work through and find constructive solutions so we can find a good outcome for both our countries".
Wang and Pompeo discussed a range of issues, such as North Korea and the trade war.
Trump also called off a meeting with Pompeo in August, due to a lag in the negotiations.
Pompeo's trip to Pyongyang followed a stalemate as North Korea resisted Washington's demands for irreversible steps to give up its nuclear arsenal, including a complete inventory of its weapons and facilities.
Up to $260 billion worth of Chinese imports to the United States have been hit by tariffs and President Donald Trump has hinted he "could go all the way to 500", which would include all goods and products going into the country.
Still, Wang's remarks made clear that China was most concerned about recent USA moves to improve ties with the democratically run island of Taiwan, which Beijing considers a province.
North Korea's state newspaper, Rodong Sinmun, featured eight photos of the meeting on its front page, including shots of Kim and Pompeo smiling and shaking hands, as well as some with Kim's sister Kim Yo Jong.
South Korean President Moon Jae-In thanked Pompeo for his visit and expressed his well-wishes for the potential upcoming summit.
"North Korea took some steps towards denuclearisation and the U.S. will face criticism from the global community if it continues to demand complete denuclearisation without any lifting of sanctions", said Yang Moo-jin, a professor at the University of North Korean Studies in Seoul.
Analysts say Washington may now consider new options as China, Russia and South Korea seek to relax sanctions.
In a statement, State Department spokeswoman Heather Nauert said Kim had invited inspectors to visit the Punggye-Ri test site in order to confirm that it had been dismantled.
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". According to the former official, the North Korean diplomats told him that denuclearization for them refers to a process by which the US also reduces its nuclear weapons, possibly worldwide. "But if you look at the approach, we are in lockstep with each of those two countries in terms of how we approach achieving the results that everyone is aimed at".
"There is room for further reductions and I expect another one percentage point cut by the year-end", Xu added.
Mazie Hirono, D-Hawaii, deflected, saying, "This is not a comprehensive FBI investigation on which we can draw conclusions". Capitol on Thursday to review the FBI's supplemental background investigation on Supreme Court nominee Brett Kavanaugh .
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