The latest incident adds to the death toll of 19 over the weekend.
The navy said it had rescued almost 4,000 people attempting to cross to Europe from Africa over the weekend, and Italian vessels are continuing to look for victims of a boat which capsized north of the Libyan coast on Sunday night.
A record number of migrants travelling by sea to Italy this year is putting enormous pressure on the Italian coastguard and navy.
At the weekend, Italy urged the EU to take over sea patrols in the Mediterranean and hinted it could stop sending its ships out to search for boats in distress.
The rescue missions, which began after a shipwreck near Italy's coast killed 366 people last October, have sparked fierce debate in Italy.