Following his arrival in Seoul from Pyongyang on Sunday, Pompeo said at a meeting with South Korean President Moon Jae-in that he had "a good productive conversation" with Kim, in talks which represented "another step forward".
Wang Yi, China's foreign minister, said trade disputes, challenges to Chinese sovereignty and criticism of Beijing's domestic and foreign policy had harmed relations.
Pompeo said that the two countries "will be having more frequent and higher-level working group discussions", but "ultimately, some of these big, hard issues have to be resolved by the nations' most senior leaders". Japan has been wary of the initiative, but South Korea has embraced it.
On a more positive note, Wang said China was still willing to solve the trade dispute with the United States through negotiations, "but they must be conducted on an equal, honest and serious basis". Pompeo didn't meet with Kim on that trip.
Specifically, Pompeo revealed that North Korea agreed to allow global inspectors to survey their nuclear and missile testing sites.
In a statement, State Department spokeswoman Heather Nauert said Kim had invited inspectors to visit the Punggye-Ri test site in order to confirm that it had been dismantled.
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.
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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".
Pompeo, however, played down the differences.
"I would certainly expect so", the official said.
The two countries have, however, been in a standoff over what the term denuclearisation means. And so there'll be tactical places where we'll have debates and disagreements. It has not taken any steps to halt nuclear weapons or missile development.
Pompeo was hit by North Korean officials a few months ago as having a "gangster-like demand for denuclearization".
Moon said a second Mr. Trump-Kim summit could be accompanied by major diplomatic developments that could contribute to the denuclearization of the Korean Peninsula and stabilizing peace. US officials have thus far said the penalties will remain in place until the North's denuclearization is fully verified.
Such an inspection has been one of the main sticking points in making progress on a denuclearisation pledge secured by US President Donald Trump and North Korean leader at the historic summit in Singapore earlier this year.
Moon also said there was a possibility of Kim holding a summit with Japanese Prime Minister Shinzo Abe.