The brief report by KCNA on Friday says the two had "a cordial talk," and Kim invited Rodman back again "any time."
The report says the two watched a basketball game together, and Kim hosted a dinner for the sports star.
The report does not say when they met or whether Rodman had left the country.
Rodman first met Kim — a basketball fan — during a visit in February to promote the sport and make a film. Rodman has suggested "basketball diplomacy" could warm relations and has called Kim an "awesome guy."
The KCNA report has no mention of Kenneth Bae, an American missionary jailed there. Before arriving in North Korea on Tuesday, Rodman did not say whether he would seek Bae's release.
Rodman once asked on his Twitter account for Kim to "do me a solid" and release Bae.
Bae was arrested in November and sentenced to 15 years of hard labour for what Pyongyang described as hostile acts against the state. Kim has the power to grant special pardons under the North's constitution.
Rodman told reporters in Beijing before his flight to Pyongyang, "I just want to meet my friend Kim, the marshal, and start a basketball league over there or something like that."
North Korea did not confirm in advance whether the basketball star and Kim would meet. Meetings between senior North Korean officials and foreigners are normally not officially confirmed or announced in advance.Suggest a correction