Ships patrolling the Mediterranean plucked more than 2,700 migrants from overcrowded and unsafe boats on Monday and rescue operations are continuing, Italy's coast guard said on Tuesday.
Ships from several countries, including those taking part in a European Union mission called "Triton", went to the aid of 18 different boats carrying 2,741 migrants on Monday, a coast guard spokeswoman said.
Almost 300 other migrants rescued two days ago arrived in the Sicilian port of Pozzallo on Tuesday aboard a ship run by Doctors Without Borders. Authorities also brought ashore a corpse in a metal coffin.
The victim had been shot dead by men travelling on another boat near the Libyan coast, according to testimony by the migrants, Italian media reported. A Sicilian court is investigating the death.
Italy has been trying to convince the EU to help it cope with waves of migrants arriving in overcrowded boats from North Africa, with official estimates putting the total at 60,000 so far this year. Almost 2,000 have died trying to make the crossing, the United Nations refugee agency has estimated.
The EU this year agreed to triple funding for sea rescues off the coasts of Italy and Greece, but the 28-nation bloc is deeply divided on how to manage the migrants once they come ashore.
EU leaders meet later this week to discuss a European Commission plan to distribute 40,000 Syrian and Eritrean asylum seekers now stuck in Italy and Greece among other EU nations.
The Commission plan also foresees creating detention centres called "hot spots" to better identify migrants and refugees and calls for those who do not qualify for asylum to be quickly deported.
With thousands of new boat arrivals each week, France is increasingly turning back migrants seeking to reach northern European countries.
Hundreds of migrants have taken shelter in or near Italy's train stations, especially in Rome and Milan. More than 100 migrants have been sleeping on rocks along the Italy-France border for almost two weeks.