The dead are thought to have either drowned or suffocated on the overcrowded fishing vessel, the navy said.
The discovery on Sunday underlined the scale of the crisis in the waters of the southern Mediterranean, where hundreds have died making the perilous journey to Europe, and tens of thousands more have been plucked from rickety boats.
More than 5,000 people were rescued this weekend, adding to the 50,000 migrants who have reached Italy from North Africa so far this year, many fleeing war and forced conscription.
Italy has called on its European Union partners to do more to help manage the near daily arrivals which have boosted support for the country's anti-immigration opposition Northern League party.
At the current rate, the figures should soon pass the record of 62,000 people who arrived by sea in 2011, when numbers swelled amid the "Arab Spring" uprisings across North Africa and the Middle East.
An Italian ship, part of the navy's migrant rescue mission Mare Nostrum or "Our Sea", was due to arrive at the Sicilian port of Pozzallo later on Monday towing the fishing boat and carrying 566 survivors.
The navy said thousands of others rescued this weekend would arrive in other ports in southern Italy over Monday and Tuesday.
Italian Prime Minister Matteo Renzi said last week the EU should take responsibility for rescuing boat migrants by investing in regional border control agency Frontex.
Northern League leader Matteo Salvini attacked Renzi and Interior Minister Angelino Alfano in a Facebook post:
"Thirty more deaths on the consciences of those who defend 'Their Seas'. Stop the departures, help them at home, now! Renzi and Alfano have blood on their shirts, don't they?"
-Reuters
