Pompeo, who arrived from North Korea, told Yi he wanted to fill him on his meetings with its leader, Kim Jong Un, and efforts to achieve the denuclearization of the Korean Peninsula.
Pompeo and Foreign Minister Wang Yi highlighted the schism after the chief United States diplomat arrived in Beijing on the final leg of an Asian trip focused on North Korea's nuclear issue.
The Beijing stop could be tense as it comes days after Vice President Mike Pence delivered a blistering speech accusing China of military aggression, commercial theft, rising human rights violations and electoral intervention against Trump. Pompeo did not meet Kim on that trip.
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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.
It added that there was an agreement to hold working-level talks to arrange a second summit between Kim and Trump.
The trip was the latest turn in a diplomatic saga that saw Trump and Kim threaten each other with nuclear war past year only for them to hold their historic summit in Singapore.
But Trump called off the trip a day later, saying North Korea hadn't made sufficient progress toward denuclearization.
Relations between Beijing and Washington have taken a sharp turn for the worse in the last month, as the tit-for-tat trade war that has seen both sides slapping tariffs on a broad range of each others' products, and both sides vowing to stand their ground.
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"We demand that the United States side immediately stop its wrong actions and words".
Mr Pompeo and North Korean leader Kim Jong-un held talks over the weekend. Mr Trump cancelled Mr Pompeo's planned trip to Pyongyang in August, citing little evidence that North Korea had followed through on any of its commitments to denuclearise.
A meeting of top USA and Chinese diplomats in Beijing to discuss North Korean nuclear disarmament has got off to a frosty start.
"There's a lot of logistics that will be required to execute that", he said at a press conference in South Korea' Seoul.
Pompeo said that Kim had agreed to allow global inspectors to visit Punggye-ri, one of the Southeast Asian nation's nuclear testing sites. 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.
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"I've never been involved in an global discussion where there weren't differences of view, not only between governments but inside of governments", he said.