"Italy is willing to try the marines at home, but in the meantime we ask for their freedom," said Interior Minister Angelino Alfano was quoted as saying by ANSA news agency.
Alfano's remarks came ahead of his meeting with UN Secretary-General Ban Ki-moon here.
Italy has been trying to rally international support among the EU, the US and NATO countries to bring home marines.
Marines Massimiliano Latorre and Salvatore Girone shot dead two fishermen off the Kerala coast in February 2012, sparking diplomatic tensions between India and Italy.
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Rome wants the marines to be tried in Italy, claiming the incident took place in international waters. However, New Delhi says it has the right to try the Italians as the victims were Indians on board an Indian fishing boat.
Lats month, UN chief Ban Ki-moon's spokesperson Martin Nesirky told reporters that the Secretary-General is "concerned that this long-standing matter between Italy and India remains unresolved and is prompting tensions between two friendly and important Member States of the Organisation.