"There have been cases in the past where smugglers tricked the immigrants and left them on Lefkada, claiming they had arrived in Italy," he said.
An official involved in the investigation told The Associated Press that most of the people on the boat were believed to be Syrians. He asked not to be identified pending official announcements.
Greece is the European Union's busiest transit point for illegal immigration.
"The new tragedy off Lefkada, with victims including young children, confirms the need to immediately implement initiatives taken by the European Union, with Greece's initiative, too, to deal with the problem of illegal migration," said government spokesman Simos Kedikoglou.
But the opposition Syriza party accused Greece and the rest of the EU of treating refugees like criminals.
"Europe is continuing its deadly pursuit of the victims of catastrophes who are seeking safe haven," the party said. "This has gone on long enough. The Mediterranean must stop being a sea of death."
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AP writer Elena Becatoros contributed.