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Power outages darkened large parts of the city during the overnight cloudburst, a river broke its banks and traffic jams brought much of Athens to a standstill in the morning rush hour.
The capital's main roads and highways were overflowing with water and public transport was severely disrupted as two subway stops were briefly shut.
"This is the worst storm since 1961. We're talking about 52 years without ever having seen such a heavy downpour in this area," meteorologist Yannis Kallianos told state television.
Police said a 27-year-old woman died of a probable heart attack after being trapped in her car in the northern suburb of Halandri.
A Reuters reporter saw another woman being rescued from her jeep as a gush of water more than a metre (yard) high swept her car away. At least five other cars in the same block were overturned and three were piled on top of each other.
Officials said more than 130 litres of rainfall per square metre swamped the neighbouring suburb of Papagou in just under three hours.
By mid-morning, rescue teams received at least 900 calls from residents whose houses were flooded and more than 90 calls from commuters marooned in their cars.
In parliament, a worker was left dangling through the glass ceiling over the assembly as she tried to contain water dripping into the room below where lawmakers were about to start debate.