Mayor Patrick Seve said 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.
The fire, the fourth deadly blaze in the Paris area since April, was quickly extinguished by firefighters, but 14 people died, mostly as a result of inhaling toxic smoke, officials said. About 500 people were in the 18-storey low-cost apartment building.
Witnesses described the screams of panicked residents or recalled leaping from windows as the blaze flared through the entrance hall of the building.
Prime Minister Dominique de Villepin said in a statement that an investigation was under way into the fire, "that could be of criminal origin."
Seve said most of those who died had tried to flee the building through the entrance, and residents who stayed inside were not injured as temperatures soared.
"It was the people who rushed outside who were met with temperatures of 300 degrees (Celsius, or 570 degrees Fahrenheit), smoke and asphyxiation," he said. "That's what caused the catastrophic toll."
Seve said witnesses claimed to have seen a group of youths who lived in the building start the fire. Police said four people had been taken in for questioning.
Jean-Luc Marx, a local government spokesman, said the apartment building had been constructed in the early 1970s as part of a state-supported plan for low-cost housing and recently underwent renovation, he said.
Firefighters said the inferno, which blackened the lobby, swept into a stairwell and raced up at least three floors, damaging several apartments. Authorities ordered about 500 people who remained inside to stay in their homes Sunday until it was deemed safe to come out.
"There was smoke, and people were screaming and wanted to jump," said resident Claude Camps, 48, who fled with his wife as the smoke had died down. "When we came out there was nothing left in the entry hall."
Ground floor resident Florence Zadi said she and her husband had leapt out of a window to safety after he opened their apartment door into a wall of smoke and quickly shut it.
About 200 firefighters rushed to the scene after the inferno erupted shortly after 1 a.m. Sunday, and medical teams set up a mobile treatment site.
Sixteen people were injured, at least 10 seriously, local fire brigade spokesman Alain Antonini said. Several were rushed to hospitals in the area. Two firefighters were among those lightly injured.
Five people were revived after suffering heart attacks, he said, and one pregnant woman who was rescued gave birth at the scene. She was taken to hospital with her newborn.
More than a dozen survivors who escaped were taken to safety at a nearby gymnasium. Authorities were preparing temporary lodging for the survivors, some of whom were expected to stay with relatives.
France has been grappling with how to deal with and prevent building fires, which have taken a heavy toll in the capital in recent months.
The government has announced a series of measures including the planned construction of new housing and the eviction of squatters from buildings considered fire hazards in the wake of three other blazes in Paris since April that killed 48 people — mostly African immigrants.
Sunday's fire did not appear to be linked to two blazes in Paris last month, one in a building frequented by squatters, the other in a rundown apartment building, Marx said.
On Friday, authorities evacuated about 140 squatters from two dilapidated Paris apartment houses, with police moving in over the protests of screaming mothers and the sobs of children. The government has listed about 60 rundown buildings in Paris as possible targets for forced evacuation.
Thousands of people marched Saturday in Paris to demand better housing for the poor and condemn the eviction plans.