President Emmanuel Macron, trying to curb what has become the most damaging scandal of his presidency, on Friday fired a top security aide who has been taken into custody after videos emerged showing him strike a young man during a demonstration in Paris in May.
On a trip to southwestern France on Thursday, Macron declined to answer questions from reporters on the subject, saying only in a video posted by a Le Figaro reporter: "I didn't come here to see you".
His supporters claimed that the punishment handed down to Benalla - suspension without pay for two weeks and a transfer to an administrative job - was appropriate.
Video footage from the protest showed Alexandre Benalla lifting a protester off the ground by his neck and covering the man's mouth before striking him over the head with his fist.
He is facing charges of violence by a public official, impersonating a police officer and the illegal use of police insignia, and complicity in unauthorised use of surveillance footage, the Paris prosecutor's office said.
Shortly afterwards he returns to the scene, attacking another protester who had been carried a short distance by police before being left alone on the ground.
Benalla, who is not a policeman and previously worked as a bodyguard, had been given permission to "observe police operations" in central Paris during a day off on the May 1 public holiday, Macron's office said.
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After the suspension, Benalla was brought back into the president's immediate entourage.
The president's office brushed off accusations that it had responded only because the almost three-month-old videos had become public.
"I'm surprised he hasn't resigned", said conservative politician Jean-Christophe Lagarde, adding that if Mr Benalla did not resign himself, the President should remove him or risk the drama becoming "an affair of state".
Opposition parties condemned the presidency's handling of the matter, arguing the punishment was too lenient and that the incident should have been referred promptly to judicial authorities.
"The feeling is that at the Elysee people think they're above everything", Wauquiez said.
Some lawmakers in Macron's centrist party also called for Benalla to be dismissed. "Our work must stop immediately and the prime minister must come and explain this", said Christian Jacob of the right-wing Republicans party.
Labour unions hold demonstrations every year on May 1 in France and clashes with police are not uncommon.