Pompeo, who met with Kim during the Easter weekend earlier this month, told the ABC News TV channel that the goal of the US administration was "complete, verifiable, irreversible denuclearization" with North Korea.
"He [Kim] agreed that he was prepared to talk about that and to lay out a map that would help us achieve that objective," he said.
Pompeo's talks with the North Korean leader were aimed at laying the groundwork for the upcoming summit between US President Donald Trump and Kim.
Trump said earlier at a campaign rally in Michigan that a meeting with Kim could happen over the next three or four weeks.