Most of the dead were between 18-25 years old, with one person among the six injured still fighting for their lives. Authorities said the bar was crowded with young partygoers.
The fire, which was was apparently sparked by birthday cake candles, was France's deadliest blaze in a decade.
“There wasn't an explosion, it was candles used for a birthday party,” a senior police official told AFP.
The flames ignited the polystyrene ceiling of the basement room where the celebrations were taking place, putting off a toxic mix of gasses that poisoned the victims, police said.
The blaze started at around midnight at the Au Cuba Libre bar in the city centre, and the firemen were at the scene by 00:20 am.
“A fire broke out in a bar in the city centre of Rouen this evening, according to an initial investigation, 13 are dead and six are injured, and more than 50 firemen attended the scene,” Interior Minister Bernard Cazeneuve said in a statement.
Prime Minister Manuel Valls expressed "deep sadness at the tragedy that claimed 13 young lives."
The blaze was France's deadliest since September 2005 when an apartment building fire in the Paris suburb of L'Hay-les-Roses killed 18 people.
- with AFP