Hamburg: A UN tribunal on Monday, while hearing Italian marines' case here, asked India and Italy to immediately suspend all legal cases which may aggravate the issue.
The International Tribunal on Law of the Sea (ITLOS) also sought initial report from both Italy and India by September 24 into the incident, PTI reported.
The tribunal passed its ruling on Italy's plea that two of its marines accused of killing Indian fishermen in 2012 should be handed over by India and tried in their own country.
India had earlier told the UN tribunal that it is ready to complete within four months the trial of two Italian marines accused of killing two Indian fishermen off Kerala's coast if Italy cooperates.
Italy had dragged India to International Tribunal on Law of the Sea (ITLOS) accusing delay in the trial of February 15, 2012, incident in which marines Massimiliano Latorre and Salvatore Girone, who were on board ship 'Enrica Lexie', allegedly killed two Indian fishermen.
"I have been instructed to state that India is prepared to guarantee that the decision of the Special Court could be handed down within four months from the date on which the hearings open, if Italy were to cooperate and withdraw its objections to the procedure before the Indian Supreme Court," Indian representative Alain Pellet told the tribunal.
India's representative told the tribunal that the marines "used automatic weapons without warning and shot in head and stomach of the two fishermen...This case is not covered by Article 97 of the United Nations Convention on the Law of the Sea but rather a double murder at sea."
The tribunal had reserved its order after hearing both sides for two days.
India also rebutted Italy's claim before the tribunal that New Delhi shut the door for a diplomatic solution to the marines issue and also that there was any back channel discussions between the senior Prime Ministerial advisers and Italian representative.
Italy has based its appeal on a UN law that grants jurisdiction in such cases to the country that owns the ship involved in any incident at sea.
The marines, Massimiliano Latorre and Salvatore Girone, who were on board the oil tanker "Enrica Lexie", are accused of killing two unarmed Indian fishermen off the Kerala coast on February 15, 2012. Italy maintains that the shooting took place in international waters and that the fishermen were mistaken for pirates.
Sergeant Girone is out on bail in India and sergeant Latorre has been given permission by the Supreme Court to stay in Italy for another six months for medical treatment.
The Italian government's version was short, straightforward and misleading, India said in the tribunal hearing at Hamburg.
India has also challenged Italy's contention that it has kept Sergeant Girone as a "hostage". "It is surprising that Italy is insensitive to the interests and plight of the victims of crime and is adopting a discriminatory attitude," India said in its submission.
With PTI inputs