The latest figures, announced on the navy's official Twitter feed, highlighted the scale of the problem just days after Italy's government said almost as many migrants had arrived so far this year as in the whole of 2013.
The navy said it had picked up around 1,300 migrants today as part of a major ongoing operation to save the lives of thousands of immigrants heading for Europe in overcrowded and rickety boats.
Yesterday, navy vessels plucked 1,443 people from boats, one of which was carrying 264 children, it said.
La Repubblica daily said most of the migrants were Syrian and Egyptian, speaking of "an exodus without end towards the coast of Sicily".
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Italy has long borne the brunt of migrants making the crossing from North Africa to Europe, but EU border agency Frontex says there has been a significant rise in numbers in recent months.
The Italian government this week put the number of migrant arrivals at over 39,000 so far this year -- not far off the 43,000 registered in the whole of 2013.
Earlier this month, however, at least 14 died when a boat sank between Libya and Italy.
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 due to clement weather conditions and growing lawlessness.