Mayor Patrick Seve said on Sunday three victims were children and warned that the toll “probably will rise further”.
About 15 other people were injured in the blaze in the town of L’Hay-les-Roses, south of Paris.
Sunday morning’s fire brings the number of deaths in recent serious blazes in the French capital to nearly 40.
About 160 firefighters tackled the fire which broke out in the entrance hall of the 18-storey building at about 1am on Sunday (2300 GMT Saturday), a French fire service spokesman said.
He said most of the victims were choked by fumes. The fire was brought under control in about three hours.
“The assumption of a criminal cause of the fire is strong”
Residents from all 110 flats in the block were evacuated, with many heading for a nearby public gymnasium.
It was the third major fire to hit the Paris area in 10 days, with the other two already killing 24 people, mostly Africans, and raising questions over fire safety and the treatment of immigrants.
But officials said the latest fire was in no way similar to the other two.
Residents from all 110 flats were
“This is a housing block and has nothing to do with the fires in Paris squats,” he said.
Four people were arrested after the fire, police said, releasing no details on them.
Town mayor Patrick Seve said witnesses described seeing youths set fire to letter boxes in the entrance hall of the building.
“The assumption of a criminal cause of the fire is strong,” local police chief Jean-Luc Marx said.
On 26 August, 17 people including 14 children died when fire broke out in a rundown apartment building housing African immigrants near the Austerlitz station on the left bank of the Seine.
Jacques Chirac has demanded
Three days later, seven other African immigrants were killed in another blaze in a rundown building in Paris, amid a growing public debate over housing for the poor and the government’s crackdown on illegal nationals.
Thousands of protesters demonstrated in central Paris on Saturday to demand proper housing for poor African immigrants in the aftermath of the deadly fires.
Organisers said nearly 10,000 people – many of them Africans – marched with banners from the site of the first fire. Police put the figure at 5000.
After the last fire less than a week ago, President Jacques Chirac demanded action on fire safety to prevent further tragedies.