ATHENS, June 3 (Reuters) - Hundreds of migrants were rescued from a sinking ship off the island of Crete in the southern Mediterranean on Friday, the Greek coastguard said, saying it was impossible to speculate how many could still be unaccounted for.

The death toll in the southern Mediterranean has mounted in recent weeks by migrants attempting sea crossings from North Africa to Europe this year. More than 2,000 people have died.

Greek authorities said 340 people were rescued, but four bodies were also recovered in a location some 75 nautical miles off southern Crete, in territory which falls under Egypt's search and rescue jurisdiction.

There was no immediate word on how many people may be missing and Greek coastguard officials refused to speculate. Greek media carried unsourced accounts the vessel was carrying anything between 500 and 700 people. It was not immediately clear where the boat had sailed from.

"From some scattered accounts we have heard (from those rescued) they set off from the African coastline," coastguard spokesman Nikos Lagkadianos told Reuters.

Merchant ships sailing in the area assisted in the operation, with about 242 people rescued taken to Italy and others to Egypt, Turkey and Malta, the Greek coastguard said.

Hundreds of thousands of mainly Syrian refugees crossed the short but precarious sea corridor to Greece from Turkey last year in small inflatable boats, but that route was effectively sealed after an EU-Turkey clampdown in March.

Now, warm weather and calmer seas in the Mediterranean have led to a surge in recent weeks in the number of people trying to cross to Italy from Libya, where people-smugglers operate with relative impunity.

Boats on this much longer journey risk being blown off course to islands such as Crete. Friday's incident was the third in a week involving migrant rescues or landings on the island.

(Reporting by George Georgiopoulos and Angeliki Koutantou Editing by Jeremy Gaunt)