Indian Prime Minister Manmohan Singh said Italy's refusal to send the two Italian naval guards back to India to face trial for killing two fishermen was "unacceptable," a report by The Times of India said.
The two guards are facing trial in a special court in New Delhi on charges they killed two fishermen off the Kerala state coast in February 2012.
The marines were guarding an Italian oil tanker off India's southwestern coast when the shooting happened. The fishermen were allegedly thought to be pirates, a Press Trust of India report said at the time.
India says the fishermen, Selestian Valentine and Ajesh Pinky, were unarmed.
Italy maintains the Indian fishing boat behaved aggressively and ignored warning shots from the guards on the oil tanker Enrica Lexie.
A diplomatic row quickly ensued after the arrest of the guards by Indian maritime authorities, who took the marines to the city of Kollam in Kerala.
Rome says the incident happened in international waters where the Indians don't have jurisdiction and that Italian nationals must be tried in Italy. However, in January India's Supreme Court rejected the Italian government's case for transferring the marines who had been out on bail since June.
The Kerala High Court granted conditional freedom to Latorre Massimiliano and Salvatore Girone on a surety of around $200,000 each and on condition they surrender their passports, The Times of India reported.
The marines also were under strict reporting orders and had to present themselves to the police daily, as well as remain within 6 miles of the main police station in Kochi -- formerly Cochin -- in Kerala.
The marines' trip to Italy was their second since their arrest in February 2012. India's Supreme Court allowed the men to go home for Christmas for two weeks, a report by the BBC said.
A civil case over the shooting deaths was settled in late April when each family of the dead fishermen accepted around $190,000 as compensation and for dropping the charges, a Press Trust of India report said.
But Indian authorities didn't drop the criminal case, for which the marines remain charged.
Italy has complained in the past of the long time Indian authorities are taking to move the case to trial.
India's External Affairs Minister Salman Khurshid said he will take up the latest developments with Italy, The Times of India reported.
"We will study and take a rightful, informed position," he said.
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