The coast guard said the rescues were carried out by military vessels from Italy, Spain, Ireland, Britain as well as a boat run by humanitarian personnel.
The Irish naval vessel Le Eithne was involved in at least six of the operations today, rescuing nearly 600 migrants from inflatable rubber dinghies that needed help in the waters northwest of Libya, according to an Irish military statement.
About 100 of the migrants were being brought to the tiny island of Lampedusa, off Sicily. Authorities were determining which larger, southern Italian ports would receive the others tomorrow.
Satellite phones are used to call for help from the Italian coast guard, which then requests that naval vessels or cargo ships in the area come to the migrants' aid. Some days this year have seen thousands of migrants rescued from many boats.
So far this year, some 60,000 migrants saved by ships in a multi-nation search and rescue mission have been brought to Italian ports.
Many seek asylum from wars or persecution in Africa or the Middle East, and hope to reach families in northern Europe. Italy wants northern European countries to take in fixed numbers of migrants. EU discussions about Italy's appeal have so far yielded plans for such help on a voluntary basis.