A bench of justices P Sathasivam and B S Chauhan, which had delivered on March 21 verdict, refused to review its verdict on Dutt's plea.
Dutt, who was granted four weeks more time to surrender to undergo remaining three-and-a-half-year jail term, will have to surrender before jail authorities on May 16.
With the dismissal of review plea, 53-year-old Dutt has got only one option of getting relief from the court by filing a curative petition.
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 Dutt by a designated TADA court in 2006 and ruled out his release on probation, saying the "nature" of his offence was "serious".
Dutt was convicted by the TADA court for illegal possession 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.
The bench also dismissed similar pleas filed by other six convicts in the case. Other six convicts, who filed review petitions are Yusuf Mohsin Nulwalla, Khalil Ahmed Sayed Ali Nazir, Mohamed Dawood Yusuf Khan, Shaikh Asif Yusuf, Muzammil Umar Kadri and Mohd Ahmed Shaikh.