The navy said 500 people had been pulled to safety and seven bodies recovered, but rescue operations were continuing and the death toll could rise.
The navy’s Bettica patrol boat spotted “a boat in precarious conditions off the coast of Libya with numerous migrants aboard,” it said in a statement.
“Shortly afterwards the boat overturned due to overcrowding. The Bettica, which had arrived nearby, threw life-rafts and jackets” to the migrants in the water, while another navy ship in the area sent a helicopter and rescue boats.
The latest arrivals bring the number of people rescued and brought to Italy since the start of the year to nearly 40,000, according to data released by the UN’s refugee agency (UNHCR) earlier this week.
Some 5,600 people were rescued from the Mediterranean on Monday and Tuesday alone.
The nationalities of those rescued were not immediately available.
The overwhelming majority of those arriving in Italy so far this year have been from sub-Saharan Africa.
Officials say there is no sign yet of Middle Eastern refugees switching to the Libyan route to Europe following moves to restrict access from Turkey via the Greek islands.