The talks lasted almost three hours and it was uncertain whether Pompeo would meet Kim Jong Un.
The top USA diplomat, who will be staying overnight in the North Korean capital for the first time, said he looked forward to a "very productive" encounter.
North Korea is looking for a venue in Switzerland for a possible second summit between its leader Kim Jong Un and U.S. President Donald Trump, diplomatic sources said Thursday.
"I'm confident what he intended there was, 'We did reduce the threat, ' " Pompeo said last week at a Senate Appropriations subcommittee hearing.
Trump's statements on the return of the remains of missing US troops have also been problematic.
The real impact of the Chemical Material Institute's expansion depends on any agreements Trump and Kim may have reached at their June summit in Singapore.
Both issues are considered essential tests of whether Kim is serious about negotiations.
"When are they going to hand us that piece of paper?"
Secretary of State Mike Pompeo is in Pyongyang to discuss the next steps toward denuclearization following the summit in Singapore.
However, the USA department of state said this did not represent any easing on its stance toward denuclearization. "The more you come, more trust we can build between one another".
The U.S. delegation includes several State Department officials and other members of the administration.
He was met at the Pyongyang airport by Kim Yong Chol, a senior ruling party official and former intelligence chief, and Foreign Minister Ri Yong Ho to begin his third visit since April and first since the June 12 summit.
"The president has made it hard to walk away from the talks even in the North is just stalling and prevaricating again", said another United States official familiar with the talks, pointing to Trump's tweets that North Korea no longer poses nuclear threats.
"Goodwill gestures between the Koreas can be compared to rocking back and forth in a rocking chair - it feels good, but you aren't really moving forward", said Bong Young-shik, a North Korea expert at Yonsei University in Seoul.
News reports over the weekend cited U.S. intelligence sources as questioning the North's commitment to abandoning its nuclear arsenal.
Pompeo's talk will be closely watched in the region.
North Korea has said it will not comply with Tokyo's demand for a resolution of the issue of Japanese citizens abducted by the North decades ago unless Japan lifts unilateral economic sanctions, sources close to bilateral ties said Thursday.