"The bodies of three men discovered on Saturday, aged 28, 58, and 35, have been identified by their families," Nikos Papaefstathiou, head of the National Health Operations Centre, told AFP.
"We are still searching for at least three people reported missing," he added.
Two of the bodies found Saturday were fished out of the gulf of Eleusis, near the town of Mandra west of Athens, by port police.
The bodies were those of two men, aged 35 and 55, a police official said.
Meanwhile in Mandra itself, rescue workers uncovered a third body buried in the mud.
The freak flood struck early on Wednesday the towns of Mandra, Nea Peramos and Megara, some 50 kilometres (30 miles) west of Athens.
Before the latest discoveries, the flood toll stood at 16 dead and six missing.
Local authorities have begun tallying the damage but with the emphasis still on clearing roads and searching for the missing, there is no clear indication of the cost.
The mayor of Mandra said some 2,000 homes and businesses had been gutted, and the Megara mayor said another 500 homes had been hit in his area. Even the local cemetery was submerged in mud, with tombstones broken and strewn about.
The Athens authorities and civil groups have been distributing food and water in Mandra.
"For the third day, there isn't a single open shop in Mandra, we don't have water, (and) we haven't washed since Wednesday," local shop owner Evangelos Peppas told AFP on Friday.
Most of the victims were drowned, carried away by the floodwaters and mudslides, or trapped in flooded cars or basements.
Some local residents spoke of a "tsunami".
Experts have said ill-conceived building in the area -- some of it by local municipal authorities -- meant this was a disaster waiting to happen.
Corrective drainage works for the area were approved in 2016 but work has yet to begin.
Stricken areas will request EU solidarity funds, the Athens governor's office said.
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![Ana Estrada suffered from polymyositis, an incurable disease that weakens muscles [Elias Alfageme/GDA via AP]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Ana Estrada suffered from polymyositis, an incurable disease that weakens muscles [Elias Alfageme/GDA via AP]")
