In his petition filed through advocate Hari Shankar, Dutt also sought release of his passport, impounded by the designated anti-terrorism court of Mumbai, to enable his trip abroad.
Dutt's passport has been impounded by the court as a condition for his release on bail, granted by the apex court, pending its decision on his petition challenging his conviction and six-year sentence for possessing illegal firearms in the run-up to the 1993 serial terror bombings in Mumbai.
On Monday, the apex court had refused permission to Samir Hingora, a Hindi film producer convicted in the bombings case, to go abroad.
Refusing permission, Chief Justice K.G. Balakrishnan said if he was so keen to go abroad, he should first spend the remaining term of his nine-year sentence in a prison.
Hingora, who has already spent a little over five years in the Arthur Road jail in Mumbai, was granted bail by the apex court earlier.
He was given a nine-year jail term by the anti-terrorism court of Special Judge P.D. Kode for supplying arms to Dutt through gangster Abu salem on the orders of Anees Ibrahim, brother of fugitive don Dawood Ibrahim.