Distress calls were also made from 22 different boats on Friday, many off Libya but also off the southern Italian coast.
The total number of people rescued in 24 hours is one of the highest in recent years but the coastguard could not confirm if it was a record.
So far, the busiest days this year have been the rescue of 3791 migrants on April 12 and 3690 on May 2.
The 17 bodies were found on three inflatable dinghies, from which more than 300 other migrants were rescued alive, the Italian navy said.
The rescue operations on Friday were led by the Italian coastguard and included the help of Italian, German and Irish naval ships working under the auspices of the EU's Frontex border agency.
Overall, more than 40,400 boat migrants - many of them fleeing conflict and poverty in countries such as Syria and Eritrea - have arrived in Italy since the start of the year, similar to the same period last year.
So far this year, about 1770 migrants have perished on the hazardous journey to Europe, according to a latest International Organisation for Migration report which does not include Friday's rescue.

