Top diplomats from China and the US engaged in a frosty exchange on Monday as US Secretary Mike Pompeo declared the two powers were stuck in "fundamental disagreement" over a range of issues from trade to China's domestic and foreign policies.
Unlike a similar trip in June, Chinese President Xi Jinping granted no audience to the US secretary of state.
"These actions have affected the mutual trust between both sides, and have cast a shadow over the prospects for China-U.S. relations, which completely go against the interest of our two peoples".
"We had a good, productive conversation", Pompeo said about the almost two-hour-long talks.
Despite Kim's talk of denuclearization during his first summit with Trump, he has yet to allow any outside inspectors into his country.
The possibility of a summit between Kim and Japanese Prime Minister Shinzo Abe is also "open", Moon said, adding: "A new order is being created on the Korean peninsula".
The Secretary of State did not meet Kim on that trip.
"We demand that the USA side stop this kind of mistaken action", he said.
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"You have to question why North Korea is pushing so hard for that end-of-war declaration", he added.
Pompeo's bodyguard was also ordered to leave his weapon behind during the negotiations.
Pompeo had said the goal of his meeting with North Korea was "to make sure we understand what each side is truly trying to achieve. and how we can deliver against the commitments that were made" in Singapore where Kim and Trump held their historic summit earlier this year.
Trump, tweeting from Washington shortly after Pompeo left North Korea, cited progress Pompeo had made on agreements Trump and Kim reached at their June summit in Singapore and said, "I look forward to seeing Chairman Kim again, in the near future". He also said that Seoul must cooperate with the USA and other concerned nations on "dismantling the last Cold War on Earth".
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.
North Korea so far has suspended nuclear and missile tests, freed three American prisoners and dismantled parts of a missile engine facility and tunnel entrances at a nuclear test site.
Pompeo declined to comment on the status of talks over Yongbyon or the details of negotiations generally, saying "we're not going to talk about where we are in these negotiations, except for things we have agreed to release with the North Koreans". A series of diplomatic understandings on Taiwan - in which the Communist Party tolerates American weapons sales while the USA accepts Beijing as the capital of "one China" - underpin more than four decades of relations between the two sides. According to the former official, the North Korean diplomats told him that denuclearization for them refers to a process by which the USA also reduces its nuclear weapons, possibly worldwide.
High-level exchanges between the two countries have been frozen, including a planned diplomatic and security meeting between US Secretary of Defence James Mattis and Chinese defence minister Wei Fenghe originally scheduled for mid-October in Beijing.