Chinese State Councilor and Foreign Minister Wang Yi on Monday met with visiting U.S. Secretary of State Mike Pompeo, saying that China and the United States should "follow the right path of win-win cooperation, rather than go astray toward conflict and confrontation".
Earlier this year, the U.S. and North Korea began talks over Mr Kim's controversial nuclear weapons programme.
"We demand the U.S. stop the unwarranted accusations and wrongdoings against China immediately", the top Chinese diplomat said, adding that the two countries should pursue cooperation "and not descend into conflict and confrontation".
"China is committed to developing a good relationship with the US". Washington and Beijing "should and must make the correct choices", Yang said.
The Secretary of State did not meet Kim on that trip.
"Kim Jong Un expressed satisfaction over the productive and wonderful talks with Mike Pompeo at which mutual stands were fully understood and opinions exchanged", North Korean news agency KCNA said.
Pompeo's bodyguard was also ordered to leave his weapon behind during the negotiations.
Pompeo told reporters in Pyongyang the two "had a great, great visit" and that Trump sent his regards.
"Progress made on Singapore Summit Agreements!"
Pompeo retorted that "the issues that you characterised, we have a fundamental disagreement".
Pompeo said "he agreed with Chairman Kim to hold the second US-North Korea summit at the earliest date possible", South Korea's presidential office said in a statement, although no specific time or location has yet been agreed. He and Biegun both said they expected meetings at the working level to begin soon and become quite frequent before the next summit.
Weakening support for USA -led sanctions - from countries including Russian Federation and China, but also South Korea - has also led to a growing sense that Pompeo is spending more and more of his time just trying to keep existing restrictions in place.
Last month, Mr Putin invited Mr Kim to visit his country but details about where and when the talks could take place have yet to be decided. Pompeo was in Tokyo for talks with Japanese officials ahead of his trip to North Korea. He pledged the Trump administration would coordinate and unify its strategy for denuclearisation with its allies. Japan has been wary of the initiative, but South Korea has embraced it.
In Pompeo's last trip to Pyongyang in July, North Korea denounced him for making "gangster-like demands". The North has rejected that and South Korea has suggested it may not be a necessary next step.
Wang expressed his hope that Pompeo's Beijing visit would play a positive role in supporting healthy bilateral ties.
"There is room for further reductions and I expect another one percentage point cut by the year-end", Xu added.
Washington and Pyongyang have sparred over the exact terms of the vaguely-worded agreement in Singapore, with the USA pushing to maintain sanctions and pressure against the North until its "final, fully verified denuclearisation". "That is a necessary component of getting to the best deliverable".
The U.S. says denuclearization means North Korea giving up its weapons.
Pompeo is on a whistle-stop tour around Asia mainly focused on North Korea's nuclear program, but upon arrival in Beijing, the agenda swiftly pivoted to the burgeoning acrimony between the world's two biggest economies, sparked by PresidentDonald Trump's trade war and fueled by his allegations that the Chinese government is "meddling" in next month's midterm elections.
Despite Kim's talk of denuclearization during his first summit with Trump, he has yet to allow any outside inspectors into his country.