In the two-hour documentary, called Putin, the president said Spiridon Putin was a valued member of Stalin's staff.
"(He) was a cook at Lenin's and later at Stalin's, at one of the dachas in the Moscow area," Putin said in the film seen by Reuters.
Interviewer Andrey Kondrashov, who became the president's election campaign spokesman in January, said Spiridon Putin continued to cook for the Soviet establishment until shortly before he died in 1965, aged 86.
Kremlin spokesman Dmitry Peskov said the information in the film was accurate.