Reports say the refugees were fleeing to Italy from Somalia, Ethiopia and Eritrea in four boats which were ill-equipped for the journey.
Italy’s President Sergio Mattarella said several hundred people appear to have died.
He said Europe needed to reflect in the face of “yet another tragedy in the Mediterranean in which, it seems, several hundred people have died.”
The Italian coastguard said earlier they knew nothing about the reported disaster, and Médecins Sans Frontières have been unable to confirm the news to The Independent.
Earlier on Monday morning, the Italian coastguard said108 refugees had been saved and six bodies recovered from a semi-submerged rubber dinghy on Sunday.
Separately, 33 refugees were rescued overnight off eastern coast of Sicily.
The reported tragedy comes almost a year after a fishing boat crowded with refugees sank in the Mediterranean, with around 800 people trapped inside.
Italy vowed to raise the shipwreck from the sea floor, to recover the corpses out of respect for the dead.
EU policymakers have been criticised of “killing by neglect” after they cut rescue missions in the Mediterranean.
The scaling back of search and rescue operations “created the conditions that led to massive loss of life,” according to a report.