The top court today rejected appeals filed by two film producers seeking more time for the actor to surrender. "We had already said that no application for extension of time will be entertained," the court said while refusing to accept the pleas.
Last week, the court had dismissed the actor's petition that his conviction in the case be reconsidered.
The court had sentenced Mr Dutt to five years in jail in March this year for possessing firearms supplied by men who executed the Mumbai bombings in 1993 that killed more than 200 people.
On April 17, Mr Dutt moved court seeking six more months to surrender to allow him to finish pending films. But the court rejected his plea and gave him four weeks to wrap up his work.
Mr Dutt has already served 18 months of his sentence but was released on bail while his case was appealed. He now has to serve the remaining three-and-a-half-years of his term.