The talks lasted almost three hours and it was uncertain whether Mr Pompeo would meet Mr Kim.
The President told me he believes that Chairman Kim sees a different, brighter future for the people of North Korea.
Pomepo said yes and added, "I'm looking forward to our time together today".
"Our leaders made commitments at the Singapore summit on the complete denuclearization of North Korea and outlined what a transformed US-DPRK relationship could look like", he said while still en route, according to comments relayed to reporters on his plane by spokeswoman Heather Nauert.
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She next faces Italy's Camila Giorgi who saved a match point to beat Katerina Siniakova of the Czech Republic 3-6, 7-6 (8/6), 6-2. She then broke back to level the third set at 4-4, but Rodina immediately earned another break and served out the victory.
Pompeo is expected to discuss the return of the remains of US soldiers killed during the 1950-53 Korean War.
Both issues are considered essential tests of whether Mr Kim is serious about negotiations.
"Work is ongoing to deceive us on the number of facilities, the number of weapons, the number of missiles", one senior U.S. intelligence official said to NBC News.
He said relations between the USA and North Korea have "dramatically shifted" in North Korea's favor over the past few months.
Although the talks have yielded nothing so far, Trump has spent the weeks since his summit celebrating it as a major success: "We signed a wonderful paper saying they're going to denuclearize their whole thing".
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Chinese defense ministry spokesman Wu Qian, asked last week whether China had again requested THAAD be withdrawn in the light of the Trump-Kim summit, said it is "resolutely opposed to the United States deploying THAAD in South Korea".
Up until recently it had maintained North Korea needs to achieve complete, verifiable and irreversible denuclearization (CVID).
Much of the work took place in May-shortly after a meeting between North and South Korean leaders that supposedly ended with a mutual commitment to officially end the Korean War and eliminate nuclear weapons from the Korean Peninsula. Lee, who plans to bring two or three North Korean players to the Asian Games, said he was impressed with "No. 9 and No. 7 on Team Peace, " referring to North Korea's Ri Jong Ok and Jang Mi Kyong. Longer-term, the Koreas have vowed to improve the North's aging railways and roads.
A day after the summit, Trump announced that the USA was canceling joint military exercises with South Korea that the North has traditionally called practice for an invasion.
Pompeo's talks, which resume on Saturday, will be closely watched in the region.
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In retaliation to the THAAD deployment, Beijing imposed unofficial boycotts on South Korean businesses and banned group tours to South Korea. North Korea's government, which is constantly concerned about increasing North Koreans' awareness of the outside world, would be just as likely to hit the brakes on goodwill gestures and exchanges if it decides that economic and security benefits aren't coming soon, Bong said.