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6 year oldConfirming media reports of the secret meeting in Pyongyang, Mr Trump said it had gone "very smoothly".
The surprise visit marks the highest-level contact between the United States and North Korea since 2000.
Mr Trump is expected to hold a summit with Mr Kim by June. Details are being worked out, the US president said.
South Korea has also signalled that it may pursue a formal resolution of the longstanding conflict on the peninsula. President Moon Jae-in and Mr Kim are due to meet next week.
The US president earlier gave his "blessing" for the talks between the South and North to discuss a peace treaty to formally end the 1950-1953 Korean War.
Mr Pompeo's trip took place after he was nominated by Mr Trump to replace Rex Tillerson as secretary of state.
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