The migrants, who were aboard 13 vessels, were saved in the central Mediterranean by ships from the Italian coast guard, the Italian and British navies, merchant ships and vessels operated by non-government organizations, a statement said.
Another 1,300 were rescued on Wednesday.
The voyage from Libya across the Mediterranean to Italy is currently the main route to Europe for migrants.
A record 181,000 made the journey last year, most on flimsy boats run by people-smugglers.
More than 5,000 are believed to have died attempting the crossing in 2016.
In the latest in a series of measures pushed by the European Union to stop migrants reaching Europe, Italy launched a new fund on Wednesday to help African countries control their borders. (Courtesy Reuters)