53-year-old Dutt filed an application before special TADA Judge G A Sanap in Mumbai seeking permission to surrender before the Yerwada jail in Pune in the 1993 Mumbai blasts case instead of giving himself up before the special court in south Mumbai.
Dutt, whose conviction under the Arms Act was upheld by the Supreme Court recently, is supposed to surrender before May 16.
"The applicant (Dutt) is facing threat to life from fundamentalist groups and those with vested interests," the application said.
It further claimed that the actor wanted to avoid a situation of the past when media persons and camera persons had chased his vehicle from Mumbai to Pune last time he was taken to jail after the TADA court convicted him.
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"The media vehicles had chased the applicant's vehicle for 120 kilometres in the past," the application said.
A bench of justices B S Chauhan and Dipak Misra refused to hear the plea of a film producer, who sought more time for Dutt to surrender in order to complete two films which are under production.
Dutt was convicted by the TADA court for illegally possessing a 9 mm pistol and an AK-56 rifle, which were part of a consignment of weapons and explosives brought to India for coordinated serial blasts that killed 257 people and injured over 700 in 1993.