US Secretary of State Mike Pompeo and Chinese Foreign Minister Wang Yi before their meeting in Beijing on Monday.
In a sign of the modest objectives of the trip, Pompeo told a reporter en route to Japan that one of his goals would be to "make sure that we understand what each side is truly trying to achieve", a comment that signaled the two countries were still a long way off from detailed negotiations on verified disarmament.
"Yeah, so we had a great, great visit this morning", Pompeo replied. "I will surely tell you in private about our conversation".
Pompeo responded that the United States has its own concerns about China's actions, and that he looked forward to discussing them during Monday's talks.
Another planned trip by Pompeo to Pyongyang was scrapped after what Trump said was insufficient progress towards implementing the terms of the Singapore declaration.
During a closed meeting with President Moon Jae-in, Pompeo said he and Kim agreed to arrange the second US-North Korea summit "at the earliest possible date" and to continue to discuss the specifics of date and location, Moon's office said earlier.
"The optimistic would say that [North Korean leader Kim Jong-un] needs it for a domestic audience so he can change his ways and have a new approach; the pessimist would say it's another way to split the allies apart", Eyre added.
Pompeo and Wang did find common ground in opposing the nuclear threat from North Korea.
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However, I wouldn't be surprised to see Alexis Sanchez axed on Saturday as his shocking form continues. After the game, he liked a picture of himself which had the caption: "It's time for Mourinho to go".
A key issue highlighted by one former US official who has spoken to North Korean officials in recent months is that the definition Kim's regime has of denuclearization is far more expansive than it is for the U.S.
"I am really pleased for this opportunity".
The country's state newspaper, Rodong Sinmun, featured eight photos of the meeting on its front page, including various shots of Kim and Pompeo smiling and shaking hands - and some with Kim's sister Kim Yo Jong in attendance.
Pompeo is meeting Chinese Foreign Minister Wang Yi and his predecessor Yang Jiechi, . but not President Xi Jinping.
Since the denuclearization 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 June 12 Trump-Kim summit that many had hoped would jump-start the effort.
After Mr Pompeo left North Korea in July, hailing progress, Mr Kim's government denounced him for making "gangster-like demands".
"But we do think right that this is a place where ultimately some of these big hard issues have to be resolved by the nation's most senior leaders and hope to have those presented in a way that the two leaders can resolve them when they get together". "After having a nice meeting, we can enjoy a meal together".
"It's a long process", Pompeo told reporters.
Mr Pompeo described his fourth trip to the North Korean capital as "another step forward to denuclearisation".
The trip was the latest turn in a diplomatic saga that saw Trump and Kim threaten each other with nuclear war previous year only for them to hold their historic summit in Singapore.