More than 2,000 migrants were rescued from five wooden boats in the Mediterranean on Saturday and as many as seven other vessels have been reported at sea, the privately funded Migrant Offshore Aid Station (MOAS) and Italy's coastguard said.

"MOAS coordinated the rescue of over 2,000 people together with Italian, Irish and Germany ships," the group tweeted. The migrants were packed onto wooden fishing boats in the Mediterranean off the Libyan coast.

Italy's coastguard, which coordinates sea rescue efforts in from Rome, could not confirm the number of migrants who had been saved so far, but said about a dozen different migrant boats had been reported and rescue operations were ongoing.

"We have several assets at work," a coastguard spokesman said.

During the first five months of the year, there were 46,500 sea arrivals in Italy, a 12 percent increase on the same period of last year, the UN refugee agency said. Italy's government projects 200,000 will come this year, up from 170,000 in 2014.

The summer months are usually the busiest period for departures because the calm seas make the crossing easier.

This year growing anarchy in Libya -- the last point on one of the main transit routes to Europe -- is giving free hand to people smugglers who make an average of 80,000 euros ($89,000) from each boatload, according to an ongoing investigation by an Italian court.

MOAS, which is operating a privately funded rescue operation with Doctors without Borders, said its Phoenix ship plucked 372 mostly Eritreans from one boat.

The Italian navy said one of its ships was still trying to remove about 560 from a wooden boat, while another navy ship has finished rescuing 316 from yet another.

(Reporting by Steve Scherer; Editing by Toby Chopra)