The 53-year-old was sentenced in March to serve five years in jail for illegally owning weapons including an AK-56 in a case linked to the 1993 bomb blasts. He will have to serve a little over three years of that as he has already spent 18 months in prison.
The Supreme Court had ruled that he should be jailed by April 18. At an emotional press conference last month, Sanjay Dutt had said would not appeal against his sentence.
The actor is currently in the midst of several film shoots - according to some reports, between Rs 70 to 100 crore are tied up in Bollywood projects fronted by him.
He has maintained that he knew nothing about the bombing plot and that he asked for the guns to protect his family after receiving threats during the city's communal riots.
Three other petitioners in the Mumbai blasts case, including a 71-year-old woman, have also sought more time to surrender. Their cases, too, will be heard by the court today.
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