A vacation bench of the apex court, comprising Justices G S Singhvi and C K Prasad asked the West Bengal Government to respond within four months to a petition filed by Ansari.
Ansari has challenged his conviction and death sentence.
On May 10, the Supreme Court had stayed the death sentence of Jamiluddin Nasir, who was also convicted in the same case.
Nasir and Ansari were sentenced to death for the attack by a Kolkata Court.
The attack by a group of terrorists on January 22, 2002 left six policemen dead.
The shooting incident in the city raised many questions, especially the risk of Bangladesh being used for cross-border terrorism.
Ansari is suspected to be connected with the militant Harkat-ul-Jehad-e-Islami outfit, which is active in Bangladesh.