Pompeo, Chinese counterpart exchange criticism during meeting in Beijing

Kim Jong Un and Donald Trump shake hands during their historic summit in Singapore back in June

"We had a good, productive conversation", Pompeo said about the almost two-hour-long talks. But that wasn't an advance on comments Trump made last month in NY, when he said he wanted to meet Kim "very soon".

"I would assume there are negotiations going on over specifics - somewhere there are people meeting, " said Dean Cheng, a senior research fellow at the Heritage Foundation in Washington.

"It's a long process", Pompeo told reporters.

"Both the leaders believe there's real progress that can be made, substantive progress that can be made at the next summit", Pompeo said.

The US official said earlier on Monday that "great progress" had been made with Kim Jong-un, and that work is being done to schedule a second summit with US President Donald Trump.

Pompeo tweeted Monday that he was heading to China to work on a "final, fully-verified" denuclearization of North Korea. He and Biegun both said they expected meetings at the working level to begin soon and become quite frequent before the next summit.

"We urge the U.S.to immediately stop its misguided comments and actions", Wang said.

One clear victor from the diplomatic back-and-forth in recent months is Kim: The North Korean leader derives enormous domestic benefit from being seen as a respected head of state meeting with a US president and his top deputies, and not just the dictator of a rogue, isolated regime.

Kim made a commitment to allow inspectors into both sites when he met South Korean President Moon Jae-in last month, but experts said it was important to have him explicitly reiterate that promise to Pompeo. Pompeo did not meet Kim on that trip. "South Korea alliance and secure the withdrawal of the 28,500 US troops based in the South".

Pompeo has refused to discuss details of negotiations, including a USA position on North Korea's demand for a formal end to the Korean War and a proposal from Seoul for such a declaration to be accompanied by a shutdown of the North's main known nuclear facility. In June, NBC News reported that an updated intelligence assessment concluded that North Korea was stepping up production of fuel for nuclear weapons at secret sites across the country.

Given the delicate nature of talks with North Korea, it's possible that Pompeo and his hosts reached agreements not yet made public.

Pompeo, however, played down the differences. "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".

"We really hope we can deliver some good outcomes from that when the summit takes place", he added. "That is a necessary component of getting to the best deliverable".

Pompeo did not say when inspectors would be allowed to Punggye-ri, and the State Department did not respond when asked if they would be Americans or others from worldwide nuclear bodies. The North Korean leader said progress is being made in implementing the goals of the first summit, and he "expressed his gratitude to President Trump for making honest effort to this end", KCNA said.

Attention now centers on how China views what Pompeo called a "good and productive" meeting, . and how Beijing will cooperate on North Korea's denuclearization process.

The supposedly autonomous Chinese territory of Hong Kong last month declined a scheduled port visit by U.S. Navy ship, and a Chinese admiral canceled a planned visit to the U.S. Just last week, China pulled out of a planned top-level defense meeting. 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.

After that inter-Korean summit, Kim also said he was prepared to permanently dismantle his country's main nuclear site at Yongbyon, but only if the United States took "corresponding steps" to build trust.

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