The marines, who were guards on an oil tanker off India's western coast last year, face a criminal trial in New Delhi over the killing of two unarmed Indian fishermen.
The Supreme Court in New Delhi said it had allowed the marines to travel to Italy in February on Ambassador Daniele Mancini's personal undertaking so the marines could vote in national elections, a report by The Times of India said.
But the fishermen haven't returned to India and the Supreme Court said it would report April 2 on Mancini's diplomatic status and to what extent he was protected from prosecution in India.
"The (court's) interim order passed March 14 directing Daniele Mancini not to leave India without prior permission of the court is extended until further orders," the court said.
The three-judge Supreme Court said Mancini waived immunity by giving an undertaking to a court that the marines would return to India after several weeks.
In the escalating diplomatic row India put airport security on alert last week should Mancini attempt to leave the country.
The move elicited a strong rebuke from the Italian government, which pointed out under the Vienna Convention no foreign authority can withdraw diplomatic immunity from accredited envoys.
But India's government stood behind the earlier Supreme Court decision.
"We have conveyed to Italy that while we are conscious of the Vienna Convention, we are bound by the directions given by the Supreme Court," Foreign Ministry spokesman Syed Akbaruddin said.
Officials, including Sonia Gandhi, the Italian-born president of the main opposition Congress Party, in the Indian Parliament, are backing the government, the Press Trust of India said.
"The defiance of the Italian government on the question of the two marines and its betrayal of a commitment to our Supreme Court is outright unacceptable," Gandhi said, addressing the Congress Parliamentary Party.
"No country can, should or will be allowed to take India for granted. All means must be pursued to ensure that the commitment made by the Italian government to our Supreme Court is honored," she said.
The row between Rome and New Delhi has been going on since the arrest of the marines off the Kerala state coast in February 2012. Indian maritime authorities picked up the marines after the shooting deaths of two fishermen the guards claim they mistook for pirates, a Press Trust of India report said at the time.
Italy maintains the Indian fishing boat behaved aggressively toward the Enrica Lexie oil tanker and ignored warning shots from guards who became suspicious of the fishing boat.
A civil case over the deaths was settled in late April when each family of the dead fishermen accepted around $190,000 as compensation and for dropping the charges.
However, Indian authorities are continuing with a criminal case, for which the marines remain charged and await their trial in a special court in New Delhi.
Even though Italy may have breached international law by breaking its promise, the ambassador's diplomatic protection remains, analysts have argued.
The U.K. government backed down on threats to lift the immunity of the Ecuadorean Embassy in London after WikiLeaks founder Julian Assange took shelter there last year, the BBC said.
India may opt for a face-saving expulsion of the Italian ambassador, the BBC report said.