Roads turned into raging torrents of mud and debris, with drivers scrambling out as their cars were washed away.
Many of the dead were elderly people found inside their homes.
'Everything is lost. The disaster is biblical,' Mandra Mayor Yianna Krikouki told state broadcaster ERT.
Torrential rain is expected to continue on Thursday with the risk of further damage.
'This is a very difficult moment for our country. We mourn the deaths of 14 people in what is a great disaster. ... It is the wish of all of us that this number does not increase,' Prime Minister Alexis Tsipras said in a televised address.
Twelve of the people killed - four women and eight men - were found in or near Mandra, a small town on the western outskirts of Athens that was hardest-hit by the flood.
The coast guard recovered the bodies of two more men believed to have been swept out to sea by the flood.
Floodwater carrying debris charged toward the coast, sinking fishing boats in a small harbor. Several people were being treated in a hospital for various injuries, including hypothermia.
There were fears the death toll could rise further as rescue crews searched flooded homes and streets on the western outskirts of Athens.
The flooding came after a severe overnight storm brought driving rain to the area. Roads turned into muddy rivers that carried away vehicles, tossing them into piles on roadsides and against fences and buildings.

Several walls from yards and low buildings collapsed, filling the streets with rubble.
The fire department said it had received more than 600 calls for help pumping water out of buildings and had rescued 86 people trapped in vehicles and homes.
It said it had deployed 190 firefighters with 55 vehicles. All fire services across the wider Athens area had been put on alert as more bad weather was forecast.











Comment: This has actually become a rather common sight in Greece (and the wider eastern Med) in recent years, where deluges have repeatedly inundated coastal towns and cities.
- Samothraki in Greece floods after 270mm (10 inches) of rain in 3 hours (2017)
- Floods in Greece leave 1 dead (2016)
- Greece flash floods: 4 dead, 1 missing after torrential rainfall (2016)
For a snapshot of the extreme weather occurring around the world, check out our Earth Changes Summary video for October 2017: