BEIJING -- Chinese officials appealed to U.S. Secretary of State Mike Pompeo on Monday to repair relations they said have been damaged by U.S. tariff hikes and support for Taiwan, as their governments press North Korea to give up its nuclear weapons.

Pompeo said at the start of his talks with Foreign Minister Wang Yi that Washington has a "fundamental disagreement" and "great concerns" about Chinese actions and looked forward to discussing them. Reporters were then ushered from the room.

The polite but edgy tone underscored the plunge in U.S.-Chinese relations as the administration of U.S. President Donald Trump confronts Beijing over its technology policies and territorial claims in the South China Sea. Trump also approved a weapons sale to Taiwan, the self-ruled island the Communist mainland claims as its own territory, and sanctioned a Chinese company and its leader over an arms purchase from Russia.

Those developments came as the countries have raised tariffs on tens of billions of dollars of each other's goods in a dispute over U.S. complaints that Beijing steals or pressures companies to hand over technology.

At the same time, the United States and China are co-operating on efforts to pressure North Korean leader Kim Jong Un to give up his country's nuclear weapons and long-range missile programs.

Pompeo met Wang and Yang Jiechi, a senior Cabinet official and former foreign minister, after talks Sunday with Kim in North Korea's capital, Pyongyang. Pompeo also visited Japan and South Korea, where he said Monday in Seoul that there had been "significant progress" toward an agreement for the North to give up its nuclear weapons.

Wang appealed to Pompeo to cease actions that Beijing sees as threatening its interests in order to avoid disrupting co-operation over North Korea and other issues.

"While the U.S. side has constantly escalated trade frictions with China, it has also taken actions regarding Taiwan that harm China's core interests," Wang said.

In their later meeting, Yang expressed Chinese frustration with Washington while avoiding specifics, telling Pompeo relations are "facing challenges." Washington and Beijing "should and must make the correct choices," Yang said.

"We hope the United States and China can meet each other halfway and conscientiously fulfil the important consensus reached by the leaders of both countries," Yang said.

In Seoul, Pompeo said he and Kim had agreed to soon begin working-level talks on details of denuclearization and placement of international inspectors at one of North Korea's main nuclear facilities.

Pompeo said they came close to finalizing a date and venue for the next Kim-Trump meeting.

"It's a long process," Pompeo told reporters. "We made significant progress. We'll continue to make significant progress and we are further along in making that progress than any administration in an awfully long time."

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."

Pompeo said he and Kim had gotten "pretty close" to fixing the logistics for the summit but stressed that "sometimes that last inch is hard to close."

"Most importantly, both the leaders believe there is real progress that can be made, substantive progress that can be made at the next summit and so we are going to get it at a time that works for each of the two leaders and at a place that works for both of them," he said.

North Korea's state-run news agency KCNA, meanwhile, said Monday that Kim had "expressed his will and conviction that a great progress would surely be made in solving the issues of utmost concern of the world."

In an early Monday dispatch, KCNA called the talks "productive and wonderful" and said that "mutual stands were fully understood and opinions exchanged."

In Seoul, Pompeo said Kim is expected soon to name Deputy Foreign Minister Choe Son Hui as a counterpart for his new special envoy for North Korea, former Ford executive Stephen Biegun, who accompanied him on the trip. He and Biegun both said they expected meetings at the working level to begin soon and become quite frequent before the next summit.

"We are starting to see a first wave of actions we can take on all four pillars of the Singapore communique," said Biegun. He is to work with South Korea, Japan, China, Russia and other countries that have an interest in the talks.

In Pyongyang on Sunday, Pompeo and Kim met for about 3 1/2 hours, first in a business session and then in a 90-minute luncheon that the North Korean leader hosted at a state guesthouse.

Before visiting Pyongyang, Pompeo held talks in Tokyo with Japan's prime minister. He pledged the Trump administration would co-ordinate and unify its strategy for denuclearization with its allies. Japan has been wary of the initiative, but South Korea has embraced it.

Pompeo has refused to discuss details of negotiations, including a U.S. 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.

The United States and Japan have pushed for the North to turn over a list of its nuclear sites to be dismantled as a next step in the process. The North has rejected that and South Korea has suggested it may not be a necessary next step.

Pompeo, however, played down the differences.

"I've never been involved in an international discussion where there weren't differences of view, not only between governments but inside of governments," he said. "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. And so there'll be tactical places where we'll have debates and disagreements. That is a necessary component of getting to the best deliverable."

"But with respect to our relationship with the Republic of Korea and Japan on this issue, I have found that we are in lockstep on the most important issues and how to approach them," Pompeo said.

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.

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. It has not taken any steps to halt nuclear weapons or missile development.

The North has accused Washington of making "unilateral and gangster-like" demands on denuclearization and has insisted that sanctions should be lifted before any progress in nuclear talks. U.S. officials have thus far said the penalties will remain in place until the North's denuclearization is fully verified.

Also on Monday, South Korean President Moon Jae-in said he expects Kim to travel to Russia and for Chinese President Xi Jinping to visit North Korea soon amid a global diplomatic push to resolve the nuclear crisis.

Moon said a second Trump-Kim summit could be accompanied by major diplomatic developments that could contribute to the denuclearization of the Korean Peninsula and stabilizing peace.

Moon also said there was a possibility of Kim holding a summit with Japanese Prime Minister Shinzo Abe.