Last month the judges ordered the Bollywood star to surrender by April 18 after reducing his sentence to five years from six.
Sanjay Dutt has asked the court for a month’s extension to hand himself in, citing work commitments.
The actor was convicted in 2006 of buying weapons from bombers who attacked Mumbai.
Sanjay Dutt spent 20 months in jail.
The serial bombings killed 257 people and wounded 713 others.
Reports say the actor is trying to finish work on a number of films before returning to prison.
Sanjay Dutt, one of Bollywood’s most bankable stars, is hugely popular for his role of a loveable gangster in the Munnabhai movies. He has also dabbled in politics.
In 2006, a special anti-terror court convicted 100 people for the blasts. Twelve were given the death penalty and 20 others sentenced to life imprisonment.
Sanjay Dutt, the most high-profile among the convicts, was originally charged with five offences, including criminal conspiracy and possession of illegal weapons.
The trial court found the star guilty of illegally possessing a rifle and a pistol but cleared him of conspiracy.
The son of a Hindu father and a Muslim mother, Sanjay Dutt said the weapons were necessary in order to defend his family during the Hindu-Muslim rioting of 1993 which followed the destruction by Hindu zealots of the Babri mosque in the northern town of Ayodhya.
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