Although it was not a record, the number saved was one of the highest ever recorded in a single day, and raised fears that the tide of desperate people trying to reach Europe has not been slowed by recent disasters.
Italian coastguards said 3,690 migrants were rescued on Saturday without giving details of today's ongoing operations.
The rescue of a record 3,791 migrants was coordinated on April 12 and another 2,850 the following day.
Video released by the coastguard showed migrants crammed onto a small boat that was intercepted on Saturday. The migrants are later seen clambering aboard a rescue vessel.
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Saturday's operations in the Mediterranean involved four Italian coastguard vessels, two Italian navy ships and two customs boats, as well as four cargo ships and tugs.
The Italian frigate Bersagliere took 778 migrants on board while the patrol boat Vega plucked another 675 from the water.
French patrol boat Commandant Birot, which was sent last week to boost the EU's Operation Triton patrols dealing with the influx of migrant boats, also picked up 219 people off the coast of Libya Saturday.
It was due to dock Sunday at 5:00 pm (15H00 GMT) in the port of Crotone in Calabria in the south of Italy, and sailors were to pass two suspected traffickers on to the Italian police.
Most of the migrants rescued Saturday were being taken to Sicily or southern Italy, while some have already landed on the Italian island of Lampedusa.
Several hundred migrants, mostly Africans but also including many fleeing the civil war in Syria, set out from Libya every day on rickety boats hoping to make it to Europe.