Another three people were killed and 10 were injured in the collapse of several houses, firemen told Algerian radio on Sunday.
Two sailors were rescued, a civil protection official said. The dead sailor was aboard a Turkish cargo ship, while the two other shipwrecked boats belonged to the Algerian shipping company CNAM.
One of them was driven ashore by high seas, landing at a suburban district of Algiers along the airport road to the east.
Fishing boats were also tossed by the storm, including one that sank in the port of Algiers, an AFP photographer reported.
The Algerian coast guard and navy have launched a massive search and rescue mission backed by a military plane and helicopter, the radio said.
Weathermen said 140mm of rain had fallen in 48 hours across several parts of northern, central and eastern Algeria.