The 66-year-old leader had not been seen in public since mid-August, missing two key occasions - the 60th anniversary of the founding of North Korea and Korean Thanksgiving.
U.S. and South Korean officials said Kim suffered a stroke, but North Korean officials steadfastly denied he was ill.
Kim's absence from the public eye is believed to be his longest since assuming leadership of communist North Korea after his father's death in 1994.
KCNA's last mention of Kim making a public appearance was in mid-August. While the reports from Pyongyang had Kim sending greetings to Russian President Dmitry Medvedev and to Chinese leaders, there had been no mention of him appearing in public until Saturday.
The reports said Kim congratulated the two soccer teams from Kim Il Sung University and the Pyongyang University of Railways afterward.
Kim praised the student athletes, saying: "The revolutionary and militant students in our country are good at art and sporting activities while devoting all their wisdom and enthusiasm to the study of science for the country and the people," KCNA said.
The university's 62nd anniversary took place on Oct. 1, but the report did not say when the game was held.