About 480 people, thought to have come from north Africa, arrived on Lampedusa island on one boat – a new record.
Another boatload of about 190 reached the same tiny island, while a third group of about 130 made it to Sicily.
Italy believes few are genuine political refugees and that most are fleeing poverty.
Italy and Libya signed an accord in July agreeing to mount joint sea, air and land patrols from mid-September.
Italy is also pushing for reception centres to be set up in Libya to stem the tide of “boat people” crossing from North Africa.
Libya has some 9,654km (6,000 miles) of maritime and desert frontiers and lacks equipment and personnel to patrol them effectively.
An unknown number drown or die aboard the boats while attempting to cross to Europe every year.