Pompeo arrived at Pyongyang's Sunan Airport on Friday afternoon, where Kim and other officials, including Foreign Minister Ri Yong Ho, Kim Chang Son, a senior official at the State Affairs Commission, and others were at the tarmac, ready to greet him and the USA delegation, South Korean news service EDaily reported.
The talks lasted almost three hours and it was uncertain whether Mr Pompeo would meet Mr Kim.
The last basketball friendly took place in 2003 in Pyongyang when a gym bankrolled by the South's Hyundai business group opened in the North's capital.
Late last month, 38 North, a USA -based North Korea watchdog, reported the North was making improvements at one of the country's nuclear research centres at a "rapid pace" despite Kim's pledge to denuclearize the Korean peninsula. "We will have good outcomes (at the Asian Games) if we join efforts", said Lee Moon-Kyu, a South Korean coach who led one of the women's teams at Wednesday's match.
Mr Pompeo would try to agree on at least an initial list of nuclear sites and an inventory that could be checked against the available intelligence, U.S. intelligence officials told Reuters.
One hoped-for breakthrough during his visit would be the return of the remains of US GIs killed during the 1950-53 Korean War.
Meantime, a South Korean newspaper reported that Pompeo brought a CD with the Elton John song "Rocket Man" to give to Kim. During their summit, the United States and North Korean delegations watched a four-minute video, made in the style of a Hollywood trailer, setting out the North's stark choice: conflict with a powerful enemy or a peaceful and prosperous future as America's (denuclearised) partner.
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"Contrary to our military's suspension of joint Korea-U.S. military exercises, North Korea is conducting military exercises on a scale similar to previous years", Kim said.
"If they're serious, then we can get down to the business of defining the terms of final denuclearisation", said one official.
Pompeo is set to reach Pyongyang on Friday for further talks on denuclearization of the country.
President Trump offered a clue of his expectations of the meeting earlier on Thursday, saying that if progress is not made with North Korea, "we'll go back to the other way" - a possible reference to his administration's more hardline stance prior to the current round of negotiations.
Over the past quarter-century, North Korea has frustrated or outfoxed USA administrations that have attempted to stop and reverse its weapons development through diplomacy and sanctions.
Pompeo's talk will be closely watched in the region. 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.