Pompeo held talks with North Korean leader Kim Jong Un in Pyongyang, before landing in Seoul on a whirlwind diplomatic visit to the region.
What did Pompeo and Kim agree to?
Pompeo and Foreign Minister Wang Yi highlighted the schism after the chief USA diplomat arrived in Beijing on the final leg of an Asian trip focused on North Korea's nuclear issue.
After meeting with Kim in Pyongyang on Sunday, Pompeo told journalists in Seoul that the leader had agreed to open up the Punggye-ri nuclear testing site to inspectors, according to a pool report.
"There's a lot of logistics that will be required to execute that", Mr Pompeo told a news briefing in Seoul before leaving for Beijing.
After a previous visit to Pyongyang in July, Pompeo had said the two foes made progress on key issues - but within hours of his departure the North condemned "gangster-like" demands from the United States, raising questions over how much the two sides really saw eye to eye.
Kim said the bilateral dialogue would continue to develop "based on the deep confidence between the two leaders", and expressed gratitude to Trump for making a honest effort to implement the agreement made at their June summit, KCNA said.
Last week, US Vice-President Mike Pence made a series of allegations on every aspect of China-US relations.
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In recent weeks, US officials have pointed to a recent meeting in Pyongyang between Kim and Moon, when North Korea committed to dismantling a missile-engine-testing site and raised the possibility of doing the same at its Yongbyon nuclear-enrichment facility.
A meeting of top USA and Chinese diplomats in Beijing to discuss North Korean nuclear disarmament has got off to a frosty start.
Pompeo replied that it was "important that we listen to each other, work through and find constructive solutions so we can find a good outcome for both our countries".
An official on Sunday's latest visit to Pyongyang with Pompeo said the trip was "better than the last time", but added: "It's going to be a long haul".
The U.S. and Japan have pushed for the North to compile and turn over a detailed list of its nuclear sites to be dismantled as a next step in the process. But Trump called off the trip a day later, saying North Korea hadn't made sufficient progress toward denuclearization.
Wang said Pompeo proposed his visit to China and the Chinese side was willing to arrange meetings.
The two diplomats had warmer words regarding efforts to curb North Korea's nuclear ambitions.
But unlike his last visit to Beijing in June, Pompeo did not have a meeting with Chinese President Xi Jinping.
Moon also said there was a possibility of Kim holding a summit with Japanese prime minister Shinzo Abe.