Nearly 3,700 migrants were rescued off Libya on Saturday and early on Sunday, the Italian coastguard says.
They were picked up from wooden and inflatable boats in 17 separate operations by Italian and French ships.
The migrants are now being taken to Italy. Rescue operations are continuing, the coastguard said.
At least 1,750 people have died this year trying to cross the Mediterranean, a 20-fold increase on the same period in 2014 when 96 people died.
Many more migrants are expected to make the crossing in the coming weeks as smugglers take advantage of calmer weather.
In a separate incident on Sunday, three people died when a boat carrying migrants to Europe sank off Egypt's coast, according to Egyptian state media. Thirty-one migrants were reportedly rescued.
At an emergency meeting last month to discuss the crisis, European Union leaders said they would triple the funding for rescue operations run by EU border agency Frontex, and threatened to target smugglers' boats with military strikes.
Italy abandoned its Mare Nostrum search-and-rescue mission last year after some EU members - including the UK - said they could not afford to fund it.
The decision was widely criticised in April after more than 800 people died when a single boat sank - the deadliest capsize recorded in the Mediterranean.
Some of the 27 survivors of the accident described being beaten by smugglers in an attempt to load more migrants.