At least 5,650 migrants were rescued on Monday as they tried to reach Europe on about 40 boats, one of the highest numbers in a single day, Italy's coast guard said.
A spokeswoman said at least nine migrants had died and a pregnant woman had been taken by helicopter to a hospital on the Italian island of Lampedusa, halfway between Sicily and the Libyan coast.
One coast guard ship rescued about 725 migrants on a single rubber boat, one of some 20 rescue operations during the day. Three were still under way and the spokeswoman said the number saved could reach 6,000 by the end of the day.
About 10 ships from the coast guard, the navy and humanitarian organisations were involved in the rescues, most of which took place some 30 miles off the coast of Libya.
Monday was the third anniversary of the sinking of a migrant boat off Lampedusa in which 386 people died.
According to the International Organisation for Migration, around 132,000 migrants have arrived in Italy since the start of the year and 3,054 have died.