A local resident, Toufik Ben Rhouma, blamed Marseille city hall for the disaster.
The first victim - a man - was pulled from the wreckage earlier on Tuesday, prosecutor Xavier Tarabeux said, adding that he needed to be identified.
Fire officials deliberately brought down most of a third building due to apprehensions the unsteady structure might cave on top of search crews and sniffer dogs combing the rubble of the other buildings.
Authorities had evacuated several dozen residents from neighbouring buildings as a precaution.
The second apartment block, which was in such a bad state that it had been condemned, was boarded up and in theory unoccupied, according to officials.
A young waiter watched the scene with tears in his eyes, anxious for news of an Italian woman who lived in the building.
Images of the buildings before they collapsed, visible on Google Street View, showed that one of the buildings was clearly in poor fix, with boarded-up windows and large visible cracks on the facade before it collapsed. "It could have been me", she said.
"The walls had been moving for several weeks and cracks had appeared", the 25-year-old philosophy student said. She told AFP that she had stayed with her parents the night before the collapse because numerous doors in the building would not close.
A Marseille fire brigade spokesman told CNN the cause of the collapse of the five-and six story buildings is not yet known.
But the incident - rare in a major Western city - has already sparked a political row over the quality of housing available to Marseille's poorest residents.
Marseille authorities launched a vast upgrade plan for the city centre in 2011. In 2011 the local authorities began a plan to renovate the city centre, but a 2015 government report suggested that 100,000 Marseille residents were living in housing unsafe to their health or security.