The marines, Massimilian Latorre and Salvatore Girone, were part of a military security team on board a cargo ship when they fired at a fishing boat in February last year, killing the two fishermen. The marines said they mistook the fishing boat for a pirate craft.
The court had allowed the marines to leave India in February to vote in Italian elections and to celebrate Easter.
Italy maintains that the shooting occurred in international waters and that Rome should have jurisdiction. India says the ship was in Indian territorial waters.
The Italian Foreign Ministry said last week that Italy would not return the marines because India's decision to try them violated their rights. It added that Italy would be open to international mediation.