Matteo Salvini, leader of the right-wing League, said Malta should accept the Aquarius but he was rejected.
Malta says the German charity SOS Méditerranée picked up the migrants in Libyan waters, which means they fall under Italy's jurisdiction.
Italy is the main entry for migrants crossing from North Africa to Europe.
The League promised voters during Italy's recent general election that it would take a tough stance on immigration.
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SOS Méditerranée, which runs the Aquarius, said the ship had been instructed by the Italian Maritime Rescue Coordination Centre to stand by in its current position, 35 nautical miles from Italy and 27 nautical miles from Malta.
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Currently operating in the Mediterranean as previously reported on Afloat is the Irish Naval Service OPV90 class L.É. Samuel Beckett. The crew recently received in Malta medals in recognition of their Operation Sophia work since deployment in April.