The boat, with 600 people on board, was intercepted south of the island of Lampedusa, Italy's southernmost point and a major landing point for migrant Mediterranean crossings from Libya.
Another person died while being rescued and two more have been evacuated by helicopter and taken to Palermo hospital in Sicily in a serious condition, the report said.
The coastguard could not be reached for comment.
ANSA said Italian authorities were first alerted by a merchant ship in the area, some 80 nautical miles (148 kilometres) from Lampedusa.
Most of them come from Eritrea, Somalia and Syria but there are also asylum-seekers arriving from Afghanistan, Pakistan and other parts of Asia as well as sub-Saharan Africa.
Earlier this month, Italian officials discovered the bodies of 45 migrants in the hold of a fishing boat, where they appeared to have suffocated after being locked in by traffickers.
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