The crisis team member, revising an earlier casualty toll, said that four people had died after jumping off their balconies and two others of cardiac arrest.
The casualties were inside Algiers, in Boumerdes to the west and Blida, 50 kilometres south of the capital.
They had been roused from their sleep by the tremor.
The official in the team set up by the health ministry told AFP that 420 people were injured, almost of whom were sent home after receiving first aid. Around 20 were kept in hospital.
But there was no significant damage caused by the quake, which hit at 5:11 am (0411 GMT), Ashur said.
The epicentre was 19 kilometres off the coast of the western district of Bologhine, said the Algerian centre for research in astrophysics and geophysics, CRAAG.
It also reported five lower magnitude aftershocks.
"This earthquake is part the normal seismic activity of Algeria, which sits on two major plates. Algeria records 100 earthquakes a month but most are not felt," CRAAG researcher Kamel Lamali said.
