The Coastguard in Greece says at least 12 immigrants drowned on Friday after their boat capsized just off an island.
Fifteen survivors were found on the shore opposite the island of Lefkada. They were being treated in hospital.
Some of the survivors said they were Syrians. They were travelling in an eight-metre inflatable dinghy.
"The immigrants called police on their mobile to say their boat was in distress," a coastguard official said.
Officials suspect the migrants had arrived to Greece several weeks ago and were heading for Italy.
The BBC reports Greece is one of the main destinations for migrants and refugees trying to enter the European Union.
Almost 400 asylum seekers drowned off the Italian island of Lampedusa in two separate incidents earlier this month.