Twelve immigrants, including four children, drowned on Friday after their boat capsized just off the Greek island of Lefkada in the Ionian Sea, the coastguard said.
Earlier reports said eight people had died.
Greece is a major gateway for immigrants trying to make their way illegally from Africa and the Middle East into the European Union.
"The immigrants called police on their mobile to say their boat was in distress," a coastguard official told Reuters.
"When we arrived we found fifteen people on the shore and picked up eight bodies, including four children."
The immigrants said there were more people on their six-meter long boat and a diver was looking for them.
The official could not immediately say how old the dead children were, how many more people were missing or what their nationality was.
Hundreds of Eritreans and Somalis drowned earlier this month when a boat sank less than a kilometer from Lampedusa, a tiny island between Sicily and Tunisia which has become the main entry point into Europe for migrant boats.
Greece, Italy and Malta have repeatedly pressed European Union partners to do more to stop a migrant crisis, which the Maltese prime minister said was turning the Mediterranean into a "cemetery."