A baby girl born on board the Italian navy patrol ship Bettica was among more than 3,000 asylum seekers and migrants landed at ports in the south of mainland Italy and on the islands of Lampedusa and Sicily.
The baby's mother had gone into labour just before leaving Libya aboard one of four barely seaworthy boats whose occupants were rescued by the Bettica.
Mother and baby were transferred to hospital on arrival but were both reported to be doing well, the navy said.
Not everyone was so lucky, at least ten migrants died, adding to an estimated total of more than 1,750 people who have perished in the waters between Libya and Italy since the start of this year.
This weekend's surge in the number of boats leaving Libya was put down to the fine weather and calm sea conditions and will have confirmed the fears of Italian officials who anticipate a record number of arrivals on their southern shores between now and September.
Last year's total of 170,000 was already unprecedented and current trends point to that figure being exceeded in 2015.
Among the ships involved in rescue ops at the weekend was the Malta-based M.Y. Phoenix, run jointly by private body Migrant Offshore Aid Station and Medecins Sans Frontieres/Doctors Without Borders.
The Phoenix, on its first mission of the year, was involved in the rescue of more than 470 people between Saturday and Monday morning, including several pregnant women and babies and a total of 45 children.
Christopher Catrambone, the American philanthropist who co-founded Moas with his wife Regina, said he had been shocked by the condition of the people they discovered packed onto a fishing boat they assisted on Sunday afternoon.
"The people were packed in so tightly that their legs had cramped and they struggled to move as we rescued them," he said.
MSF doctors treated migrants suffering from injuries sustained during beatings by people smugglers and others suffering from conditions including diabetes, dehydration and skin infections, as well as carrying out checks on the pregnant women.
MSF's Will Turner added: "The boat was absolutely crammed full. As the men, women and children we rescued curled up under blankets to sleep, there wasn't a centimetre to spare. The scale of this crisis is just heartbreaking. I wish we could do more."
The migrants landed in southern Italy will quickly be dispersed to reception centres across the country pending decisions on their future.
Aid agencies say a large number of those attempting the Mediterranean crossing have legitimate claims to asylum in Europe as they are fleeing conflict or repression in places including Syria and Eritrea.
In a rare example of conflict-wracked Libya attempting to stem the migrant flow, five boats which set off at the weekend were intercepted by the Libyan coastguard and sent to the city of Misrata, home to a detention centre for migrants.
Australian Prime Minister Tony Abbott meanwhile revealed that his officials were talking to European Union counterparts about how to stop the flow of boats.
However, the European Commission, the executive of the 28-nation EU, said that it was not aware of such talks and that Brussels would never adopt Australia's model of turning back these boats.
Australia has successfully stopped asylum-seeker boats from reaching the continent by deploying its navy to turn them back, effectively deterring other would-be migrants.
The policy has proved controversial however with critics accusing the government of ignoring its international obligations on asylum and other human rights.
People smugglers have taken advantage of the chaos gripping Libya since the 2011 uprising that toppled dictator Moamer Kadhafi.
On April 19th, some 750 migrants were killed when their trawler sank between Libya and southern Italy, sparking global outrage and demands for action.
Four days later EU leaders tripled the bloc's budget for patrols off Libya.
EU leaders are now seeking UN Security Council approval for military action against smugglers.
But rights groups have criticised Europe for focusing on patrols rather than providing asylum seekers with legal avenues to seek refuge.