At least 50,000 people have crossed from North Africa to Italy so far this year, exceeding the 40,000 who arrived in the whole of 2013, according to the Italian coastguard authorities.
That leaves the annual total set to surpass the 60,000 who made the trip in 2011 when the Arab Spring revolutions loosened border controls.
The navy said that, together with the Italian coastguard, on Friday it had saved 39 migrants from the boat that capsized about 40 nautical miles north of Libya but that it had also picked up 10 bodies.
It gave no information on the nationality of the victims or the other migrants, who have been transferred on to the Italian supply ship Etna.
The ship, carrying about 700 migrants picked up in the last few days, is heading for the Sicilian capital of Palermo where it is due to arrive today.
The surge of migrants leaving North African shores is straining the ability of the Italian navy to patrol the waters between Africa and Italy on its own.