(Updates number of migrants rescued)

By Darrin Zamit Lupi

ABOARD THE TOPAZ RESPONDER, June 23 (Reuters) - Ships manned by humanitarian organisations, the Italian navy and coast guard helped rescue about 4,500 boat migrants on Thursday as calm seas returned to the Mediterranean, prompting a surge in departures from North Africa.

Rescue operations were continuing, an Italian coast guard spokesman said. The corpse of a woman was taken from a large rubber boat, and the migrants were collected from a total of about 40 different vessels, he said.

The Topaz Responder, a ship run by the Malta-based humanitarian group Migrant Offshore Aid Station (MOAS), said earlier in the day that around two dozen migrant boats had been spotted in the sea about 20 nautical miles from the Libyan port city of Sabratha.

"The mass movement is probably the result of week-long, unfavourable weather conditions" that have come to an end, MOAS said on Twitter.

The Topaz Responder picked up 382 sub-Saharan African migrants from three different large rubber boats. The Bourbon Argos, a ship run by humanitarian group Doctors without Borders, plucked 1,139 migrants from 10 boats, and two other humanitarian vessels picked up 156 more.

The Italian navy said it had rescued 515 from two dinghies, German humanitarian group Sea-Watch said it had 100 on board, and the Italian coast guard, which coordinates rescue operations, said it had deployed several boats.

An agreement between Turkey and the EU to stop migrant departures for the Greek islands has reduced boat arrivals by 98 percent during the first five months of the year from the same period of 2015, the International Organization for Migration (IOM) said.

But arrivals in Italy continue at about the same clip as last year, and the deadly central Mediterranean route has already claimed 2,438 lives, IOM said.

Italy has been on the front line of Europe's worst immigration crisis since World War Two and now in its third year. More than 320,000 boat migrants came to Italy from North Africa in 2014-15.

As of Wednesday, 56,328 boat migrants had been brought to Italy in 2016, a 5.5 percent decrease on the same period of last year, according to the Interior Ministry.

Nigerians, Eritreans and Gambians were the top three migrant nationalities this year, the ministry said, and more than 125,000 are now living in Italian shelters. (Reporting by Darrin Zammit Lupi on the Topaz Responder migrant rescue ship and Stephanie Nebehay in Geneva; Writing by Steve Scherer; Editing by Mark Heinrich)