"The perpetrator was waiting for the soldiers to leave the barracks and head to their auto", he added.
An exchange of fire took place between the police and the suspected driver of the auto, which had ploughed into six soldiers earlier on Wednesday. Police have closed off the roads.
Two police officials said authorities are checking video surveillance of the area near the city hall in Levallois, in the north-west of the capital, to identify the vehicle and hunt down the driver. "This vehicle was waiting for them", he continued.
Patrick Balkany, the local mayor for Levallois-Perret, said he had "no doubt" the soldiers were targeted deliberately.
Police wait near the scene of the attack, a narrow alleyway.
The street is normally guarded by posts that are removed when vehicles move in and out, so the driver must have known exactly when to strike, Veillant said.
Six of the dozen or so troops were injured - two of them seriously - in the attack which is being investigated by counter-terrorism officials.
He was shot five times, while an officer was also hit by a bullet before the man was arrested, said a source close to the case.
French government spokesman Christophe Castaner said the Paris prosecutor's office has opened a counterterrorism investigation.
After reviewing video surveillance, police descended onto Paris and the surrounding area, conducting auto searches in their hunt for the attacker, the Associated Press reported on Wednesday. "Levallois is a calm place ... this is an odious aggression against our military that nobody expected".
This attack appears to be the latest in a series of incidents targeting Paris in recent months.
In April a policeman was shot dead by a man on the Champs-Elysées, who was later shot dead himself.
The injured soldiers were all the members of the anti-terrorism operation which has been deployed since the Charlie Hebdo attack in 2015 in Paris.
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