A recent three-day heat wave, in which temperatures have touched 40C, has left forests and shrub land parched, with flames fanned by the strong winds.
"We are living through an unspeakable tragedy today," said Costas Karamanlis, the Greek prime minister, who visited Zaharo late on Friday.
The government appealed to European Union countries to "send any help they can," said Spyros Flogaitis, the acting interior minister, after an emergency meeting of Greece's civil protection authority.
The Greek military has been called in to help firefighters.
In Athens, a fire broke out during the night in a park in the Filothei area, a few kilometres north of the city centre.
|"I'm one person, all alone in the dark in a blazing valley. I need help"|
Mayor of a Greek village
Five fire trucks initially sent to tackle the blaze had to call for reinforcements, the department said.
Eleven people, including three firefighters, died in mountainous villages near Zaharo, the fire department said.
Rescue crews were checking reports of several other bodies found in a mountain village in the western Peloponnese, said Nikos Diamandis, a fire department spokesman, early on Saturday.
Across the Peloponnese to the southeast, five people were burned to death on Friday near a hotel on the outskirts of the town of Areopolis - including two whose charred bodies were found locked in an embrace.
Across Greece, dozens of houses went up in flames.
Residents and local officials called television stations with desperate appeals for help.
"I'm one person, all alone in the dark in a blazing valley. I need help," said one man, whom the Mega television channel said was the mayor of Palaiochori village.
One woman in the village of Rodina, near Zaharo, told Antenna television that about 20 people, including children, were trapped in the village.
"We can see the fire in front of us. It's at our feet," said the woman, who did not give her name.
"We're choking on the smoke."