The early morning saw a coast guard vessel with 481 migrants aboard reach the southern Sicilian port of Pozzallo, while the Phoenix vessel of Maltese NGO Moas began disembarking 422 more further up the coast at Trapani.
One migrant was a newborn Cameroonian named Chris, whose mother gave birth to him on Tuesday aboard a rickety wooden boat.
Rescuers applauded as she made her way up a ladder to haul herself on to the Aquarius, a vessel chartered by SOS Mediterranee and MSF.
The little boy's father has still to attempt the hazardous trip to Europe from Libya.
MSF midwife Alice Gautreau tweeted how she cut the child's umbilical cord.
"Little Chris is doing fine, his mother too. But it would have been better for both if she had not had to give birth in the middle of the Mediterranean, surrounded by 100 men," Gautreau added.
We're all a little bit in love with these 7 pounds and 10 ounces of perfection. Happy Birthday Chris, may Europe treat you with kindness. pic.twitter.com/faEDtMliWA— MSF Sea (@MSF_Sea) July 11, 2017
Vessels from four other NGOs - Medecins sans Frontieres (MSF), SOS Mediterranee, Save the Children and ProActiva Open Arms - were on their way to Italian ports with a cargo of some 2,700 more migrants, including many children, picked up on Tuesday, those organizations said.
Italy has been urging its EU partners to make a "concrete contribution" to dealing with the crisis both in terms of trying to limit departures from Libya and also taking in a portion of those who survive the perilous journey.
Italian Prime Minister Paolo Gentiloni warned last week that his country did not have "unlimited" capacity to keep taking people having already accepted around 85,000 of the 100,000 people who have arrived this year.
EU interior ministers last week pledged to back an urgent European Commission plan to help Italy by earmarking 35 million euros ($40 million) in aid.
The issue was high on the agenda of Wednesday talks in the northeastern city of Trieste between Gentiloni, French President Emmanuel Macron and German Chancellor Angela Merkel attending a Western Balkans summit.