More than 20 people have been injured and one is missing in a disaster that local media have described as "biblical."
Residents in Mandra, one of the most affected areas, northwest of Athens, have been "trapped in their homes, the water is 1 meter (about 3 feet) high inside some houses, and (they) have no electricity and water," said Mayor Yianna Krikouki.
Speaking on Greek radio, Krikouki said there was "nothing standing in the entire area of Mandra" and the town is "now mourning its lost fellow citizens."
A state of emergency has been declared in the West Attica region, where Mandra is located. Parts of the national highway system have been destroyed, and many roads remain shut down. Hundreds of homes and businesses have been damaged.
Entire areas are without water or power. One firefighter told local media that "a large part of the electricity network is severely damaged. We are doing what we can."
More than 20 schools will remain closed Thursday. One elderly resident, who has lived in the area since the 1960s, told local media that she's never seen anything like the devastation she witnessed.
"I don't know what to do," she said to TV channel Skai. "People have drowned in this very street."
More heavy rain has been forecast, firefighter Kimon Moustakas told public broadcaster ERT. "We are here and ready to do everything we can."
Greek Prime Minister Alexis Tsipras declared three days of national mourning.
"It is a very difficult time for all of Greece," he said, according to ERT.
"I want to express my deep sorrow, sincere condolences to the families of the victims. And (I want to) pledge that we will stand by them with all the means in our disposal."
Tsipras called an emergency meeting Wednesday with relevant ministers, the head of the fire department and the Greater Athens prefect.
As many as 86 people have been rescued from floodwaters, with the injured transported to hospitals.
The fire department said it has received at least 600 calls for assistance and operations continue, according to its press office.
An Athens prosecutor has ordered an urgent preliminary investigation into the causes of the destruction. The floods were triggered by heavy rains.
European Commission President Jean-Claude Juncker expressed his condolences.
"I am saddened to learn about the many people who have lost their lives and loved ones during the deadly floods affecting central Greece. On behalf of the whole European Commission, I would like to express our full solidarity with the Greek people and authorities at this difficult time," he said in a statement.
"A tragedy in any of our member states is a tragedy for all of Europe. We stand ready to support Greece in any way we can. Our EU emergency assistance tools are at the full disposal of the authorities."
Christos Stylianides, the European commissioner for humanitarian aid and crisis management, said that his agency was in contact with the Greek authorities Wednesday.
"Europe stands by Greece," Stylianides said on Twitter.
"Our thoughts are with our fellow citizens who remain trapped and in the efforts to rescue them."