"Around 3,000 migrants were saved Tuesday during 30 operations coordinated by the coastguard," the Italian coastguard said in a statement.
After several weeks of relative calm in the stretch of Mediterranean between Italy and Libya, more than 1,100 people were rescued on Sunday and another 6,500 on Monday.
Dramatic images distributed by the Italian coastguard showed children among the survivors crammed onto an old fishing boat.
Some of the migrants jumped off the vessel in life jackets and swam towards their rescuers.
The total number of arrivals in Italy this year now stands at 112,500, according to the UN's refugee agency and the coastguard, slightly below the 116,000 recorded by the same point in 2015.
Involved in the rescue at dawn on Monday were the Italian coastguard and navy, and the Dignity 1 ship operated by the NGO Doctors Without Borders (MSF), whose spokesman Nicholas Papachrysostomou said 650 people were saved.
"Many of them had never seen the sea before. There were elderly women on board, sick people, and several children aged 13 or 4 who were travelling alone," he said.
"They were fighting each other to be rescued first, they were jumping into the water, it was hard to control the situation."
However, the drama was far from over.
"At the end of the day, the horizon was filled with boats," Papachrysostomo told AFP, speaking by phone from the Dignity 1.
"It was an extraordinary day," he added.
Another NGO, Proactiva Open Arms, described Monday as "an endless day" and "a sad record" on its Facebook page.
Among the survivors were babies and small children carried by their parents. A mother and her premature newborn were evacuated by helicopter as soon as they had been rescued.
On Tuesday morning, a woman gave birth on board the rescue ship as it made its way to the Italian coast.
She and her newborn were taken by speedboat to the island of Lampedusa, while the rest of the migrants made their way to several ports in Sicily, Sardinia and southern Italy.
The coastguard and MSF said the spike in migrant arrivals was due to improved weather conditions after a bad spell.
More than 3,100 people have died trying to reach Europe this year.