Two Italian marines serving aboard an oil tanker as part of an anti-piracy mission allegedly fired shots in 2012 that killed two Indian fishermen on a boat off India's southern Kerala state.
India detained the two marines days later and a court case is pending, while Italy has challenged India's jurisdiction over the case.
The two-day hearing opened on Monday at the Hamburg-based International Tribunal for the Law of the Sea.
Italy has demanded that India “refrain from taking or enforcing any judicial or administrative measures” against the marines.
It also asked in it submission that “restrictions on the liberty, security and movement of the marines be immediately lifted”.
India has rejected the request, arguing that the case is not a maritime dispute but “about a double murder at sea”, in which one fisherman was shot in the head and the other in the stomach.
One of the servicemen, Massimiliano Latorre, was last year allowed to temporarily return to Italy for medical treatment and is still there.
The other, Salvatore Girone, has been living at Italy's embassy in New Delhi.
In opening statements, Italy's Francesco Azzarello said the two marines had “not been charged with any crime” and had “protested their innocence throughout”.
He said the oil tanker, the MV Enrica Lexie, was in international waters at the time of the incident and accused India of an “unlawful exercise of jurisdiction over the incident, over the vessel and over the marines” whom it had arrested.
Italy argues the ship was about 20.5 nautical miles off Kerala en route from Sri Lanka to Djibouti at the time of the incident when its radar showed an unidentified craft “heading rapidly towards the MV Enrica Lexie”.
“The craft continued to head towards the Enrica Lexie despite sustained visual and auditory warnings from the Enrica Lexie and the firing of warning shots into the water” before it eventually turned away and headed towards the open sea, Italy said in a statement.
Sir Daniel Bethlehem QC, also speaking for Italy, said “the correct procedures aboard the 'Enrica Lexie' were followed in response to the suspected attack”.
“It is not established that they (the marines) caused the deaths of the two Indian fishermen,” he said.
The tribunal is expected to hand down its decision in late August.