Massimiliano Latorre and fellow marine Salvatore Girone shot the fishermen while serving as part of an anti-piracy mission off southern India in 2012 in a case that has sparked a diplomatic row between the two countries.
Both marines were barred from leaving India pending trial, but Latorre was given permission to travel to Italy for heart surgery last year. Italian reports said the surgery was a minor procedure to correct a congenital heart defect.
He had been due to return to India this month, but the Supreme Court ruled on Thursday that he could stay for another three months after his lawyers said he had developed complications.
Judge Anil R. Dave said the Italian ambassador to India had given a fresh undertaking that Latorre would fly back in July.
Girone is living at Italy's embassy in Delhi. He and Latorre say they mistook the fishing boat for a pirate vessel and fired what were intended to be warning shots.
Italy says the pair should be tried on home soil since the shootings involved an Italian-flagged vessel in what it says were international waters.
India, however, maintains the killings took place in waters under its jurisdiction.
In December, Rome threatened to withdraw its ambassador from India after a court rejected Latorre's request for medical leave, a ruling that was later overturned.
The marines were granted home visits to vote in national elections in 2013, but India was furious when the Italian government initially said it 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.