The court said the matter would be listed Friday, by which time the central government would respond to the plea of the two marines - Chief Master Sergeant Massimilano Latorre and Sergeant Salvatore Girone.
The two Italian marines on board the Italian cargo vessel Enrica Lexie shot dead two Indian fishermen Feb 15 last year, suspecting them to be pirates.
Recounting the history of their case that started with the shooting of two fishermen and the apex court Jan 18 verdict holding that Kerala had no jurisdiction to try the marines, Latorre and Girone in their petition said that "by the very nature of the things, it is likely to take some time for matter to move ahead in the present case".
Recalling that they had come back to India to face the legal proceedings after the Kerala High court in a "humane gesture" allowed them to visit their families for four weeks on the guarantee of the Italian government, the two marines said they may be permitted once again to visit their country on a similar undertaking.
If permitted to travel to Italy, the marines said they would be able to "exercise their right to vote in their home town" for the general elections that will take place Feb 24 and 25.
The marines said that on the expiry of four weeks they would return to India to face legal proceedings. They contended that no prejudice would be caused to the Indian government in the case if they were allowed to travel to their country.
Supporting the petition of the two marines, the Italian embassy in New Delhi has offered an undertaking that the marines would be kept under the "constant custody, supervision and control in Italy during this period".