While visiting the town sports centre, Mr Medvedev said a separate programme should be drawn up for building more swimming pools.
The President spoke with children training at the sports centre, discussed the Beijing Olympic results with them, congratulated them on the start of the new school year and wished them success in their studies.
Mr Medvedev later visited School No 18 in the town, where he spoke with pupils and met with former colleagues of his grandfather, who worked in Korenovsk.
Korenovsk is located 64 kilometres from Krasnodar.