Thirion said that in Trebes, the town with the most deaths, the Aude River quickly swelled from about knee-height to a destructive flood that ended up being over 6.5 meters (21 feet) deep.
Another person was killed after a house collapsed in Cuxac-d'Aude and somebody else was reportedly swept away while they were sleeping.
It is believe to be the worst flooding in the area since 1891.
An anticipated reshuffling of government ministers would not be announced while the government was focused on the flooding, the official said.
Philippe, who arrived in Aude on Monday, said in a tweet that more than 700 firefighters and seven helicopters have been dispatched to the area to help with rescue operations.
One of the victims was an elderly nun who got swept away by floodwaters.
A man rides past a damaged vehicle in the town of Villegailhenc, southern France.
The levels were still rising and expected to peak at around 9:00 pm (1900 GMT).More news: Dodgers' Fans Boo Grandal, Barnes To Start In Game 4
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As the emergency intensified, villages and towns with up to 2,000 residents were being evacuated.
At least 13 people died as violent rainstorms turned rivers into raging torrents in southwestern France on Monday in the latest episode of wild weather in Europe, officials said.
The floods were caused by several months worth of rain falling without warning in just five hours last night.
Hardest hit was the town of Trebes, located just east of the medieval walled city of Carcassonne.
Of the five people confirmed dead, a nun was swept away by the waters in Villardonnel, and two people, initially missing, were found dead in Villegailhenc.
The storms were triggered when a front of warm and humid air from the Mediterranean Sea slammed into colder air around the Massif Central mountain range, inundating an area from the eastern Pyrenees to Aveyron further north.
Damaged cars are removed from a river following heavy rains that saw rivers bursting their banks on October 15, 2018 in Villegailhenc, near Carcassone, southern France.
Men looks at scenery of damaged houses in Villegailhenc, France. However, France's weather service, Metro France, said the adverse weather had recently become more frequent and severe. Leslie has already passed over Portugal and Spain.