Chinese Foreign Minister Wang Yi told US Secretary of State Mike Pompeo at a Monday meeting in Beijing that "a shadow has been cast over the future of China-US relations".
However, experts questioned what Pompeo had achieved on Sunday on his fourth visit to Pyongyang this year.
Pompeo said he's "hopeful" worldwide inspectors would soon be allowed on select sites associated with North Korea's missile and nuclear program, and didn't comment on Pyongyang's insistence that inspectors would be allowed into the Yongbyon site only if the US took corresponding measures.
North Korea took apart the Punggye-ri facility in the country's northeast in May but has yet to allow global observers into the site to verify its claims.
"I know that you would like to discuss the North Korea issue and other relational issues with me on this visit", Wang said.
"Recently, as the US side has been constantly escalating trade friction toward China, it has also adopted a series of actions on the Taiwan issue that harm China's rights, and has made groundless criticism of China's domestic and foreign policies". Kim Yong Chol also made clear that Pompeo's preferred translator wouldn't be allowed, and his bodyguard would have to leave his weapon behind, according to a pool reporter traveling with Pompeo.
"We are still talking about Punggye-ri and Sohae 6 months after he pledged to dismantle them". The US has said that it will not make such concessions unless the North takes substantive steps to do away with nuclear weapons.
That was followed by President Donald Trump's positive note: "Progress made on Singapore summit agreements!"More news: John Terry announces his retirement
He told South Korean President Moon Jae-in on Sunday his latest trip to Pyongyang was "another step forward" to denuclearization but there are "many steps along the way".
Ms Nauert said Mr Pompeo "held productive discussions" with Kim.
But Pyongyang failed to keep its pledge to allow worldwide inspections of its demolition of the Punggye-ri site in May, fanning criticism that the move could be reversed. And the Stimson Centre's 38 North said last week that no dismantling activity was spotted since August 3.
Commenting on Pompeo's meeting with Kim, South Korean President Moon Jae-in said Kim was expected to visit Russian Federation soon.
The secretary of state also confirmed that inspectors would also be invited to a separate missile test site at Tongchang-ri, but declined to comment on which organization might be allowed in to either site.
Sceptics of Trump administration policy said it was hard to see what Pompeo had achieved.
Pompeo's hurdles were highest in Pyongyang.
"Recently, as the US side has been constantly escalating trade friction toward China, it has also adopted a series of actions on the Taiwan issue that harm China's rights and interests, and has made groundless criticism of China's domestic and foreign policies", Wang said at a joint appearance with Pompeo.More news: Indonesia considers making devastated areas mass graves
Pyongyang's official KCNA news agency was upbeat.
"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".
But it made no mention of inspections.
Pope Francis has never been to North Korea and only visited the southern part of the peninsula once, in 2014.
"China is committed to developing a good relationship with the US". "An announcement of a near-term summit would show that the Trump administration has again prioritized a flashy show over real substance", he said.
During the meeting in Beijing, Wang said China and the USA should strengthen cooperation on North Korea.
Dmitry Peskov, spokesman for Russian President Vladimir Putin, said Monday that Putin extended an invitation to Kim last month to visit Russia, and that Moscow is working on the details of where and when that meeting could happen.More news: World stocks tumble after International Monetary Fund slashes economic growth forecast
This version of the story corrects 4th paragraph to make clear that Washington has been seeking inspection of Yongbyon.