As another frantic weekend of rescues unfolded, at least 4,000 people were plucked to safety from packed fishing boats and rubber dinghies off Libya.
Mass drownings in the Mediterranean have claimed nearly 1,800 lives so far this year.
All of those rescued will be deposited at ports on Sicily or elsewhere in southern Italy in the coming days, lifting this year's total of new arrivals on Italian soil to over 50,000.
The latest batch sent the migration crisis back to the top of the political agenda with three big northern regions vowing to defy the centre-left government of Prime Minister Matteo Renzi by refusing to house any of the new arrivals.
Lombardy president Roberto Maroni said he would be writing to local mayors and prefects in his region on Monday to warn them not to accept any more "illegal immigrants" allocated by the government. Municipalities that did not tow the line would have their funding from the region cut, he said.
Giovanni Toti, the newly-elected president of Liguria, backed that stance.
"I have already said it: we will not receive any more migrants, and Lombardy, Veneto and Val d'Aosta will do the same thing."
Luca Zaia, the right-wing president of Veneto, said the region that includes Venice was: "Like a bomb ready to go off. The social tensions are absolutely crazy."
British Royal Navy ship HMS Bulwark was on Sunday engaged in an operation to save at least 500 people from four boats in waters between Italy and Libya.
The UN's refugee agency said up to 1,500 people were adrift on ten dinghies, but there was no confirmation of those figures from Italy's coastguard.
The Bulwark's action followed the rescue on Saturday of just under 3,500 migrants from 15 packed boats in a stretch of water 45 miles (70 kilometres) off the coast of Libya.
Italy's coastguard said boats from the Italian, German and Irish navies took part in the rescue operation, which was coordinated in its initial stages by Moas, a privately-funded mission operating out of Malta in partnership with the Doctors without Borders (MSF) charity.
There were no reports of casualties but one Italian navy boat which was ferrying 475 migrants to Sicily reported that it had seven pregnant women on board who will be transferred to hospital on landing.
The latest operations will lift to just over 50,000 the number of arrivals in Italy since the turn of the year and the cost and other problems involved in processing them is becoming a hot political issue.
The figure represents an increase of around ten percent on the same period last year, which, after a summer surge, ended with an unprecedented total of 170,000 migrants arriving on Italian soil.
The country's reception facilities are at breaking point with nearly 80,000 asylum seekers or recently arrived migrants currently accommodated across the country.
Story continues below…
Government attempts to get regions to open up new facilities are increasingly running into opposition; mainly from right-wing politicians but also at a grassroots level from communities which don't want refugees housed in their neighbourhoods.
The small region of Val d'Aosta in the Alps has refused to take any more, citing a lack of adequate facilities.
If Lombardy, Veneto and Liguria act on their threats to follow suit, the government will have a major problem on its hands at a time when it is also grappling with growing evidence that organised crime has been siphoning off public funds allocated for the accommodation of migrants during their processing.
According to the International Organisation for Migration (IOM), nearly 1,800 migrants have drowned attempting to make the crossing since the start of this year, including some 800 in an April sinking that was the biggest maritime disaster in the Mediterranean since World War II.
EU governments reacted by sending more boats to patrol the area.
But they have been unable to agree on a longer-term strategy to ease the migration crisis amid divisions over how to spread asylum seekers fairly across member states and how to combat traffickers.