The court will Monday begin considering a request for Massimiliano Latorre to be allowed to return to Italy to continue his recuperation following his hospitalisation in New Delhi with an ischemia -- a blood blockage that can lead to a stroke.
The 47-year-old was discharged from hospital on Sunday and is not thought to be in any immediate danger: but Foreign Minister Federica Mogherini insisted that his chances of a full recovery would be increased by being allowed home.
"Massimiliano Latorre has received excellent treatment in India but it is clear he has need of rest, peace and his family," Mogherini said on the sidelines of a political conference in Bologna.
"We hope that India's Supreme Court will listen to the medical arguments."
Latorre's lawyers will argue that the Chief Master Sergeant should be allowed to return to Italy in order to reduce the risk of a stress-induced repeat incident while he awaits the resolution of a case that has caused a diplomatic rift between the two countries.
Mogherini, who is shortly to become the new European Union foreign policy chief, added: "The initiative (by the lawyers) has the full support of the Italian government. We hope he will be able to return to Italy for the entire time he needs to fully recover."
Latorre and fellow marine Salvatore Girone are currently barred from leaving India pending a possible trial. They have been living at Italy's embassy in New Delhi.
They are accused of shooting the two fishermen while serving as part of an anti-piracy mission on an Italian-flagged oil tanker, the Enrica Lexie, off the southern Indian state of Kerala in February 2012.
The Italian sailors say they mistook the fishing boat for a pirate vessel and fired what were intended to be warning shots.
Criminal proceedings against the two men were suspended in March when India's top court agreed to consider a challenge to prosecutors' jurisdiction in the case and a request for the marines to be allowed home pending its outcome.
The marines were granted a home visit to vote in national elections last year. That ended up intensifying the diplomatic tensions as Italy briefly resisted sending the men back before finally succumbing to India's pressure in March, triggering the resignation of Italy's then-foreign minister.
Italy argues the two men should be tried on home soil since the shootings involved an Italian-flagged vessel in what it maintains were international waters. India says the killings took place in its territorial waters and the perpetrators should face Indian justice.