The suspect was not killed, and officers detained him and took him to hospital. He is a 36-year-old man, according to a city official.
Patrick Balkany, mayor of Levallois-Perret, identified the suspect as Hamou Benlatreche. Balkany said authorities don't know a motivation in the attack or whether it was directed by an outside group or if he acted alone.
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Earlier, French counterterrorism prosecutors opened an investigation after the suspect, driving a BMW, injured six soldiers by ramming them as they left their barracks in the Levallois-Perret region of the city.
The country's Minister of the Armed Forces said three of the wounded soldiers were seriously injured but were not critical.
Balkany told NBC News earlier: "Without a doubt this is a terrorist attack ... he deliberately drove out to hit the soldiers."
He added that he was saddened at the attack, which was recorded on multiple surveillance cameras.
Jean Claude Veillant, who lives in an apartment above the square where the incident occurred, said he heard "a noise and then loud cries" just before 8 a.m. (2 a.m. ET).
"My wife and I we got up and went to the balcony," said the 70-year-old. "There we saw bodies lying on the ground, soldiers were running and some soldiers were trying to help others who looked injured."