Italy asked a UN-mandated tribunal on Monday to order India to put on hold its case against two Italian marines over the 2012 incident where they allegedly killed two Indian fishermen.
Marines Massimiliano Latorre and Salvatore Girone are accused of killing the fishermen while assigned to anti-piracy duty aboard an Italian oil tanker, the Enrica Lexie, off India's coast.
The men have been held without formal charges in India, though they were allowed to return temporarily to Italy to vote in 2013 elections. Latorre was also allowed to travel home for medical treatment in September after suffering a stroke, and is still there, while Girone remains detained in India. India, which insists it has jurisdiction, wants to charge both sergeants with murder.
Italy maintains that the shooting occurred in international waters, that the fishermen were mistaken for pirates and that the case should be heard in an Italian court.
Rome took the case to international arbitration in June. Pending that arbitration, it is seeking a ruling from the International Tribunal for the Law of the Sea to lift restrictions on the movement of the marines, enabling Girone to return home and Latorre to remain there on medical leave.
It also wants the tribunal to say that India shouldn't exercise jurisdiction over the incident pending an arbitration ruling.
"Frustration, stress and deteriorating medical conditions affecting directly and indirectly the people involved threaten great prejudice to Italy's rights and mean that there is the need to address urgently this situation," Italian delegate Francesco Azzarrello told the tribunal.
Hearings are scheduled Monday and Tuesday. It wasn't immediately clear when the tribunal will rule.