The man attacked the three women, who were aged 19, 24 and 36, with two kitchen knives, severely wounding two of them, Nunez said.
Video aired on social platform X and verified by Reuters showed a man with long black hair, wearing a cream tracksuit and wielding one big knife in each hand stabbing and attempting to attack a young woman.
It is unclear if the woman was injured.
Another part of the video shows the same man lying on the ground immobilised by bystanders, while the two knives are lying nearby on a pedestrian crossing.
"It is Allah who commanded me," the man lying on the floor said.
Nunez said the man had been detained by an off-duty police officer.
"I pay tribute to him, it was a courageous act," he added.
The motive of the attack remains unknown, Nunez said, adding police could not verify the identity of the attacker, whose declarations were "incoherent" while he was being arrested.
The French anti-terrorist prosecutor's office said it was weighing whether to open an investigation.
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