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6 year oldIt is Mr Pompeo's first visit to the country since Mr Kim's historic summit with Donald Trump in Singapore.
Mr Trump has boasted of averting nuclear war, although others say the resulting agreement lacked substance.
Mr Pompeo is therefore under pressure to produce evidence Pyongyang is taking steps towards ending its programme.
The document signed in June by the two leaders - who spent much of last year trading insults - saw Mr Kim promise to rid the Korean peninsula of nuclear weapons.
However, it did not outline a timeline or how exactly this would be achieved.
Mr Pompeo told reporters before Friday's meeting he was "seeking to fill in some details on those commitments and continue the momentum toward implementation".
The former director of the CIA added that he expected North Korea to be "ready to do the same". He said he was looking forward to a "very productive" encounter.
It is unclear whether he will meet Mr Kim in person.
Mr Pompeo was met by North Korea's Foreign Minister Ri Yong-ho and Kim Yong-chol, the general known as Mr Kim's right-hand man, who was equally positive ahead of the summit.
"The more we meet, the deeper our friendship will be, I hope," he said. "The more you come, the more trust we can build between one another."
Mr Pompeo's upbeat mood appeared to continue following the two sides' first meeting, which lasted three hours.
"I'm proud of my team's work," he told waiting reporters.
Mr Pompeo simply laughed when questioned on rumours that he had brought Mr Kim an Elton John CD as a present - a reference to one of Mr Trump's favourite insults for the North Korean leader, who he repeatedly referred to as "Little Rocket Man" on social media.
The secretary of state travels on to Tokyo on Saturday to meet with Japanese and South Korean officials, following his first overnight stay in North Korea.