A massive search operation is continuing for “hundreds” of missing migrants after at least 78 drowned when a fishing boat sank off the coast of Greece.

Officials said 104 survivors were rescued after the vessel capsized about 50 miles from the southern coastal town of Pylos.

But charity Alarm Phone, which operates a network supporting rescue operations and received frantic calls from some of those on board, said up to 750 people may have been on the vessel.

Greek officials said the boat got into difficulties when its engine stopped and it began veering from side to side. It then capsized and sunk at around 2am on Wednesday.

Shortly beforehand, Alarm Phone said it spoke to someone on board who said: “The captain left on a small boat. Please, any solution.”

They also pleaded for food and water, and said the vessel had stopped moving, according to the charity.

The search for survivors continued on Thursday morning and is expected to last until at least Friday, Greek authorities said.

Six coast guard vessels, a navy frigate, a military transport plane, an air force helicopter, several private vessels and a drone from the European Union border protection agency, Frontex, are taking part in the operation.

Officials said it was unlikely the sunken boat would be recovered because the area of international waters is one of the deepest in the Mediterranean.

Alarm Phone accused Greek and other European authorities of failing to launch a rescue operation before the boat sunk, despite being “well aware of this overcrowded and unseaworthy vessel”.

The Greek coast guard denied the claim and said those on board “refused our assistance because they wanted to go to Italy”.

Spokesperson Nikos Alexiou added that they still stayed nearby “in case it needed our assistance which they had refused”.

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Aerial pictures released by the Greek coast guard showed the 20 to 30 metre-long boat hours before it sank.

Dozens of people on the upper and lower decks were seen looking up, some with arms outstretched.

Witnesses said many more women and children were below in the hold, according to local reports.

Greek authorities, who initially said 79 people had died before later revising the figure down to 78, said they could not confirm how many people were on board.

The UN’s International Organisation for Migration said initial reports suggested there were up to 400 people on the vessel.

The boat is thought to have set off from the Libyan port of Tobruk and was heading to Italy.

Greek authorities said most of the migrants were from Egypt, Syria and Pakistan.

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It comes as Libyan authorities launch a major crackdown on migrants, with several thousand – including Egyptians, Syrians, Sudanese and Pakistanis – detained.

Many Egyptians have been deported to their home country through a land crossing point.

The region is one of the main routes into Europe for refugees from the Middle East, Asia and Africa.

The UN said there have been more than 20,000 deaths and disappearances in the Mediterranean since 2014, making it the most dangerous migrant crossing in the world.