The petition claimed the officers died allegedly due to technical and maintenance failure of batteries in the submarine.
It sought the probe to ascertain whether there was a timely provision of batteries and other safety equipment.
The PIL, filed by advocates Subrata Das and N Rajaraman, also sought a direction for calling the communication between the Defence Ministry and the Navy Command relating to the maintenance of submarines, particularly Sindhuratna.
Navy Chief Admiral DK Joshi resigned following the incident taking moral responsibility.
The Navy had said human miscalculation led to the fire that broke out on cables on Sindhuratna. The probe had mentioned a deviation from standard operating procedure.
The PIL sought court's direction to the Defence Ministry to also submit the status report on the action taken by it on the requisitions concerning repairs and replacement of safety equipment of the armed forces.