A boat attempting the perilous Mediterranean crossing off a Greek island capsized killing 12 migrants.
"The immigrants called police on their mobile to say their boat was in distress," a coastguard official said.
The coastguard found 15 survivors on the shore opposite the Ionian island of Lefkada and recovered 12 bodies, four of them children aged between three and six, another official said.
Four bodies were found trapped in the seven to eight metre long fibre glass boat.
Some of the survivors said they were Syrians.
Hundreds of Eritreans and Somalis drowned earlier this month when a boat sank less than one kilometre from Lampedusa, a tiny island between Sicily and Tunisia.
Crisis-hit Greece, Italy and Malta, the EU's gate-keepers, have repeatedly pressed EU partners to do more to solve the migrant crisis.
The Maltese prime minister has said that the migrant crisis was turning the Mediterranean into a "cemetery".
Greece has long struggled with illegal immigration.
It has been worsened by a deep economic crisis that has boosted anti-immigrant sentiment among Greeks.
Athens has vowed to make the issue a priority next year, when first Greece, then Italy hold the EU's rotating presidency.
"For years now, Greece has been dealing with waves of illegal immigration but this is not only a Greek issue any more," government spokesman Simos Kedikoglou said.
"The new tragedy outside Lefkada, with young children among the victims, confirms the need to immediately implement European Union initiatives to deal with illegal immigration.
Greece is a major gateway into the European Union for migrants from Africa and the Middle East, who cross the sea often in unsafe boats.
The breakdown of order in Libya and the civil war in Syria have increased the human traffic.
