Pompeo also met with Politburo member Yang Jiechi.
"It's a long process", Pompeo told reporters Monday.
The U.S.'s top diplomat retweeted Trump's tweet touting a "good meeting" in Pyongyang.
Up to $260 billion worth of Chinese imports to the U.S. have been hit by tariffs and President Donald Trump has hinted he "could go all the way to 500", which would include all goods and products going into the country. "Progress made on Singapore Summit Agreements!"
At the weekend, the People's Bank of China effectively made a decision to pump up to US$175 billion into the economy when it reduced the reserve requirement ratios, or RRR, for commercial banks.
Secretary of State Mike Pompeo arrives at Osan Air Base in Pyeongtaek on Sunday after his Pyongyang trip.
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".
In a sign of the modest objectives of the trip, Pompeo told a reporter en route to Japan that one of his goals would be to "make sure that we understand what each side is truly trying to achieve", a comment that signaled the two countries were still a long way off from detailed negotiations on verified disarmament.
When asked for a date on the inspection, Pompeo responded: "As soon as we get it logistically worked out".
The inspectors will visit a missile engine test facility and the Punggye-ri nuclear testing site as soon as the logistics are worked out, Pompeo said. He came away from it saying the two sides had made progress, only for North Korea to denounce him for making "gangster-like" demands and raising "cancerous" issues.
"There was an exchange of stands of the top leaderships of the two countries on the issues arising in holding the second DPRK-US summit talks to be followed by an in-depth discussion of them", the KCNA said.
The challenge for the USA remains stark: American administrations for decades have been stymied by North Korean intransigence on its nuclear program, and the rapport between Trump and Kim hasn't resolved that issue.
Pompeo retorted that "the issues that you characterised, we have a fundamental disagreement".
Analysts say Washington may now consider new options as China, Russia and South Korea seek to relax sanctions.
Pompeo, however, played down the differences.
In an interview with the Washington Post, she said the North could agree to dismantle Yongbyon, its signature nuclear site. Trump said it resulted in a "special bond" between the two leaders and he was optimistic about a denuclearized future.
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. It has not taken any steps to halt nuclear weapons or missile development.
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.