The Italian Marines have been accused of shooting two fishermen from Kerala in 2012.
The government indicated on Monday that it would allow an Italian marine detained for the 2012 killing of two fishermen to fly home on medical grounds after he submitted a request to the Supreme Court.
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 RM Lodha asked the government to deliver its response by their next scheduled hearing on Friday.
"It is a case of illness and physical condition. If you have any serious objection (on the plea) you have to tell us," a bench headed by the Chief Justice said.
Senior advocates Soli Sorabjee and KTS Tulsi appeared for the Italian marines.
External Affairs Minister Sushma Swaraj later told reporters,"The application is in court, we are not opposing it."
"If the courts allow him to go home on humanitarian grounds, we will not oppose it," she added.
Ms Swaraj's comments came after the marines' counsel told the court that the Italian ambassador would sign an undertaking assuring Mr Latorre's return after two months.
The court also exempted Mr Latorre, 47, who has just been discharged from a hospital in Delhi, from appearing before a police station in the capital as stipulated in his current bail conditions.
Mr Latorre and fellow marine Salvatore Girone are currently barred from leaving India pending a possible trial and have been living at the Italian 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 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.
Mr Latorre wants to be allowed to return to Italy to continue his recuperation following his hospitalisation in New Delhi with ischemia -- a condition related to restricted blood supply that can lead to a stroke.
Although he was discharged from hospital on Sunday, outgoing Italian Foreign Minister Federica Mogherini has said Mr Latorre's chances of a full recovery will increase if he is allowed to return home.
Criminal proceedings against the duo 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 the national elections last year. When the Italian government initially said they would not send the men back, the government reacted strongly.
A subsequent U-turn, which followed intense diplomatic pressure by India, triggered the resignation of Italy's then-foreign minister.