Vessels taking part in EU border security operation Triton rescued the migrants from their rickety boats in five separate operations on Monday, following the arrival in Sicily on Saturday of 1,300 migrants, mostly from sub-Saharan Africa and Syria.
The 13 bodies were recovered by an Irish military ship after it came to the aid of one of the boats, which was carrying 522 people.
The cause of death was not yet known, the coast guard said, but migrants attempting the perilous crossing to Europe often suffer from dehydration and sun exposure.
Italy and Greece have been hard pressed to handle a massive increase in migrants fleeing conflicts and poverty in Africa and the Middle East.
More than 1,900 migrants have died this year making the dangerous journey across the Mediterranean to Europe, out of around 150,000 people who have made the crossing, the International Organization for Migration said earlier this month.