Castaner said at the site that 120 police officers and 80 firefighters took part in the search-and-rescue operation, working through the night in the pile of beams and rubble.
Authorities have not revealed the identities of the victims, and several other people remain missing.
"There's not much chance that we'll find pockets where anyone might have survived", Castaner said on Monday evening.
Emergency crews were searching for as many as eight people feared buried in the debris, Marseille public prosecutor Xavier Tarabeux added on Tuesday. Authorities said the vacant building had been deemed substandard.
Google Street View images from July show that building with boarded-up windows and damage to the facade.
People had been living in nine of the 10 apartments in one of the buildings, while a shop occupied the ground floor. He has had no news of her since Monday.
Sabine Bernasconi, the local mayor for that area of Marseille, said one of the buildings had been subject to an evacuation order.
"She was a great girl, she used to come and study at the bar", he said, without giving his name.
Sophie Dorbeaux meanwhile told AFP she had left the block on Sunday night to stay with her parents because the building's structural problems meant her door, like several others, was not opening or closing properly.
"It could have been me", the 25-year-old philosophy student said, visibly shaken.
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. However, according to neighbors, it is at the time of the tragedy could be people, particularly the homeless.
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