A day after Italy's foreign minister urged authorities to grant Massimiliano Latorre permission to head home for treatment, a Supreme Court panel headed by Chief Justice R.M. Lodha asked the Indian government to deliver its response by their next scheduled hearing on Friday.
"The application ... is in court, we are not opposing it," Foreign Minister Sushma Swaraj told reporters soon afterwards.
"If the courts allow him to go home on humanitarian grounds, we will not oppose it," she added.
Swaraj's comments came after the marines' counsel had told the court that the Italian ambassador would sign an undertaking assuring Latorre's return after two months.
The court also exempted 47-year-old Latorre, who has just been discharged from hospital in New Delhi, from appearing before a police station in the capital as stipulated in his current bail conditions.
Latorre and fellow marine Salvatore Girone are currently barred from leaving India pending a possible trial and have been living at Italy's embassy.
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.
Latorre wants to be allowed to return to Italy to continue his recuperation following his hospitalization in New Delhi with ischaemia -- a restricted blood supply that can lead to a stroke.
Although he was discharged from hospital on Sunday, the outgoing Italian Foreign Minister Federica Mogherini has said Latorre's chances of a full recovery would be increased by being allowed home.
Criminal proceedings against the pair were suspended in March when judges 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 but India was furious when the Italian government initially said they would not send the men back.
A subsequent u-turn which followed intense Indian diplomatic pressure triggered the resignation of Italy's then-foreign minister.