Doctors Without Borders (MSF) said that it saved 716 of the migrants, and had found one body.
"Around 800 people were rescued today (Friday) during eight separate operations" in the Mediterranean, said a spokesman for the coastguard, which is coordinating the operations.
The migrants were on eight boats, including two inflatables, he said.
Some 130 others were rescued on Thursday.
MSF tweeted that it had "completed the 5th rescue (operation) and now have 716 people onboard. Unfortunately, for one person we arrived too late."
The UN refugee agency has said around 61,250 migrants have reached Italy since the start of the year after crossing the Mediterranean, while 1,778 more are dead or missing.
Conflict-ravaged Libya has long been a stepping stone for migrants seeking a better life in Europe.
It has urged Europe, and particularly Italy, to supply it with the equipment it needs to monitor its southern borders, through which migrants, mostly from sub-Saharan Africa, enter the country.