Interior Minister Angelino Alfano said Italy's "Mare Nostrum" operation -- a large-scale naval deployment launched after twin shipwrecks last October-- could not continue beyond October and must be taken over by the EU border agency Frontex.
"We do not believe that Mare Nostrum, which was a short-term project, can go on for a second year. I will do my utmost to make sure Frontex and Europe take over," he said during a press conference in Rome.
"If this does not happen, the Italian government will have some decisions to make. Responsibility for the Mediterranean's borders must belong to Europe," he added.
The cost of the "Mare Nostrum" is estimated at €9 million ($12 million) a month.
According to ministry figures, close to 117,000 migrants arrived in Italy by boat between August 2013 and July 2014, with Mare Nostrum rescuing 63,000 of them.
The UN refugee agency this week said that more than 100,000 people had arrived in Italy by sea since the beginning of 2014, over half of them fleeing war, violence and persecution.
The arrival numbers are far higher than the previous record of some 60,000 arriving in 2011 at the height of the turmoil triggered by north Africa's Arab Spring revolutions.
Most of the migrants making the risky and often deadly journeys come from Eritrea, Somalia and Syria, but many others hail from across Asia and sub-Saharan Africa.