A top security aide for President Emmanuel Macron, caught on camera beating a protester, has been detained and is being questioned by authorities.
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".
Police are questioning Mr Benalla, an assistant to Mr Macron's chief of staff, over footage filmed by a student activist showing a woman and a man being beaten during the demonstrations on 1 May.
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.
Despite his official change to a desk job, Benalla was seen this month on the ground with police at several high-profile events, including the return home Monday of France's champion World Cup team, an event attended by hundreds of thousands.
"New facts that could constitute misdemeanour by Alexandre Benalla were brought to the president's attention", said an Elysée official. "This came as punishment for unacceptable behavior".
"An observer doesn't act like that", said the spokesman for the UNSA-Police union.
Opposition parties have condemned the presidency's handling of the matter, arguing the punishment was too lenient and the incident should have been referred to judicial authorities.
The president's office brushed off accusations that it had responded only because the almost three-month-old videos had become public.
Arnaud Montebourg, a former minister in former president Francois Hollande's government, recalled dismissing Benalla from his service after just a week because of a "serious professional failure".
"The feeling is that at the Elysee people think they're above everything", Wauquiez said.
"By not immediately managing a disciplinary problem, Emmanuel Macron now faces a political crisis", wrote the right-wing Le Figaro daily - which usually makes no secret of its admiration for the president. "This man is the eyes and ears of the prince (Macron)".
Mr Macron, an independent centrist, portrays himself as a relaxed liberal, but is becoming increasingly well known for his reactionary law and order policies.
Later the speaker of the lower house of parliament, Francois de Rugy, announced a parliamentary inquiry into the case.