The bodies of three women had been found by coastguards overnight but another 62 men and eight women, one of them pregnant, were rescued, it said.
It did not disclose the nationalities of those on the boat, which got into difficulties about 35 nautical miles off the Libyan coast and 140 miles from Lampedusa.
Italian authorities had moved after a call for help made by satellite phone, and informed colleagues in Libya and Malta.
The stricken boat was later spotted by a Maltese plane.
A spokeswoman for the UN refugee agency praised what he called an “extraordinary operation”, saying that without it, “another 70 people would be dead.”
“Italy fulfills a leadership role in the Mediterranean in saving lives at sea, thanks to Italy’s tradition, the preparation of its men and the means at their disposal,” Laura Boldrini told ANSA.
Sicily’s new left-wing governor, Rosario Crocetta, greeted the survivors as they arrived in Lampedusa, where he was vacationing.
“Europe must provide a response to the tragedy of Africa, and there is also the tragedy of Lampedusa, which shoulders the problems of illegal immigration on behalf of all of Europe,” Crocetta said.
When a boat carrying more than 100 Tunisian migrants sank off Lampedusa in September, rescue services managed to pluck only 56 people to safety, and the others were lost at sea.
Each year, thousands of illegal migrants, mostly from Africa, attempt the crossing of the Mediterranean in often overcrowded and unseaworthy vessels in a bid to reach the European Union.
Rome said in September that 8,000 migrants had landed on Italian beaches since the start of the year.
However the figure is a sharp drop from the figure of 60,000 last year when the Arab Spring uprisings saw a vast increase in refugees and immigrants fleeing the region for the West.
Rome attributed the decline in part to a deal with north African countries to prevent boats leaving their shores.