In his petition, Dutt sought six more months time to surrender in order to complete his unfinished films before he goes to jail.
Dutt, 53, who was directed to surrender by April 18, urged the apex court to allow him to finish shooting of his films which will take at least 196 days and submitted that he should be allowed to surrender after completion of films as huge money has been invested by the producers in these projects.
The apex court had on March 21 granted Dutt, who has already been in jail for 18 months, to surrender within four weeks to undergo the remaining prison term.
The apex court had on March 21 upheld his conviction in the 1993 Mumbai serial blasts case which it said was organised by underworld don Dawood Ibrahim and others with the involvement of Pakistan's ISI.
However, the apex court had reduced to five years the six year jail term awarded to him by a designated TADA court in 2006, ruling out his release on probation because the "nature" of his offence was "serious".
Dutt, the son of famous Bollywood couple Sunil Dutt and Nargis, was convicted by the TADA court for illegal possession a 9 mm Pistol and a AK-56 rifle which was part of the consignment of weapons and explosives brought to India for the coordinated serial blasts that killed 257 people and injured over 700.