The Italian navy said another 200 people had been rescued after the ship sank with a reported 400 people on board.
"Fourteen bodies have been recovered so far. Medical workers on the Sirio and the Grecale are providing assistance to the 200 survivors," the Italian navy said on Twitter, referring to two warships on the scene.
Two Italian coast guard vessels and several merchant ships scrambled to the area were also taking part in the high-seas rescue operation, the navy said.
Libya has long been a springboard for Africans seeking a better life in Europe and the number of illegal departures from its shores is rising.
Hundreds of migrants land in Italy almost every day, most of them asylum-seekers from Eritrea, Somalia and Syria, and many are now being picked up by Italian warships.
The latest shipwreck happened at around 1100 GMT and some 100 nautical miles (185 kilometres) south of Lampedusa island, Italy's southernmost point.
The area is closer to Libyan than to Italian shores.
Italian media reported that there had been some 400 people on board the migrant boat, which would leave dozens of people still unaccounted for.
The head of Italy's Red Cross, Francesco Rocca, said that "the European Union must act immediately, without wasting any time" and "not shirk responsibility".
ANSA news agency cited rescuers saying the boat was first spotted by a patrolling Italian coast guard plane that made an emergency call to a merchant ship in the area, which became the first on the scene.
The migrant boat later sank near an offshore oil rig, the report said. The cause is not yet known.
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