By Karolina Tagaris and Stamos Prousalis

KALAMATA, Greece (Reuters) -At least 79 migrants drowned early on Wednesday and hundreds more were feared dead or missing after their overloaded boat capsized and sank in open seas off Greece, in one of Europe's deadliest shipping disasters.

As a painstaking search for survivors continued, a European rescue support charity said it believed around 750 people were on board the 20- to 30-metre-long (65-100 foot) vessel, while the U.N.'s migration agency cited an estimate of up to 400.

Greek authorities said it was too soon to speculate on the total number.

Greece is one of the main routes into the European Union for refugees and migrants from the Middle East, Asia and Africa. Most cross over to Greek islands from nearby Turkey.

But since the previous conservative government of Kyriakos Mitsotakis introduced tougher surveillance at the country's migrant camps, increasing numbers have chosen to make a longer, more dangerous journey from Turkey to Italy via Greece.

Greek state broadcaster ERT said the boat that sank was en route for Italy, having set sail from the Libyan town of Tobruk, which lies south of the island of Crete. Greek authorities did not confirm the vessel's departure port.

Alarm Phone, which operates a trans-European network supporting rescue operations, said it received alerts from people on board a ship in distress off Greece late on Tuesday, but subsequently lost contact.

"According to the people, there were 750 people on board... We now hear reports of a shipwreck and fear they are true," it said on Twitter.

Greek authorities said it remained unclear how many the vessel was carrying when it went under, and that 104 people had been rescued by midday.

"It is not safe to give a number. We do not know how many people were in the hold," Greek coast guard spokesperson Nikos Alexiou told Greece's MEGA TV. "...There were too many people on the outer deck. It was full."

Late on Tuesday, a few hours before the boat capsized, the boat's occupants refused an offer of help, insisting on continuing their journey, the coast guard said.

The shipwreck is the deadliest off Greece this year, and among the worst in Europe. In February, 96 people died when their wooden boat smashed into rocks on Italy's Calabrian coast during a storm.

The Greek migration ministry blamed international smuggling networks for putting migrants' lives at risk, while Filippo Grandi, the U.N. High Commissioner for Refugees, called on governments to work together on creating safe pathways for people fleeing poverty and war.

INTERNATIONAL WATERS

The Greek coast guard said the ill-fated boat was first spotted late on Tuesday by EU border agency Frontex in international waters around 50 miles (80 km) southwest of the southern Greek coastal town of Pylos.

Italian authorities then alerted Greece to the vessel's presence, and the Greek coast guard approached it and offered help. But migrants packed on its outer deck "refused assistance and stated their desire to continue their voyage", according to the coast guard.

A few hours later, the vessel began veering from side to side before capsizing around 2 a.m. on Wednesday and then sinking, a government official said.

ERT TV said most of those on board were young men in their 20s. A shipping ministry official who spoke on condition of anonymity said most were from Egypt, Syria and Pakistan.

Survivors were taken to the southwestern Greek coastal town of Kalamata and were expected to be moved to a camp outside Athens, the migration ministry said.

Covered in blankets, exhausted survivors rested on mattresses at a warehouse shelter set up in Kalamata port.

Libya, which has had little stability or security since a NATO-backed uprising in 2011, is a major launching point for people seeking to reach Europe by sea. People-smuggling networks are mainly run by military factions that control coastal areas.

In recent days, security forces in Libya have cracked down on migrants with detentions and deportations. It was not clear whether the ship that sank on Wednesday departed Libya before or after the crackdowns.

Greece was at the front line of Europe's migration crisis of 2015-16, when nearly 1 million people arrived on its islands from Turkey before heading north to wealthier European states.

Numbers have fallen dramatically since a 2016 EU-Turkey deal to stem the flows. Mitsotakis' government has said its tougher stance had helped keep arrivals low.

Greece is currently led by a caretaker administration ahead of a national election on June 25 that the conservatives are expected to win.

About 72,000 refugees and migrants have arrived so far this year in Europe's front-line Mediterranean countries, according to United Nations data, with the majority landing in Italy and around 6,500 in Greece.

Nearly 1,000 people are estimated to have died or gone missing in the Mediterranean this year, according to the U.N.

(Reporting by Stamos Prousalis in Kalamata, Karolina Tagaris, Lefteris Papadimas and Renee Maltezou in Athens, Gabrielle Tetrault-Farber in Geneva and Reuters Libya Newsroom; writing by Karolina Tagaris; editing by John Stonestreet and Mark Heinrich)