PARIS, Oct 3 - The student protest movement that has spread across France is now "out of control", the Paris police chief said on Saturday, urging demonstrators to return to peaceful action and warning that authorities would respond firmly to violence and vandalism.

Riot police clashed with high school students across France on Friday and unions called for teachers to strike as President Emmanuel Macron's government battled to contain increasingly violent protests over classroom conditions and funding.

Since Monday, around 5,000 people, mostly teenagers, have been arrested nationwide and dozens injured.

Agathe Foucault, a spokesperson for the national police, told RTL radio on Saturday that more than 600 police officers had also been injured. Teachers and members of the public have been attacked, while damage to property is estimated in the tens of millions of euros.

Paris police chief Patrice Faure, in an open letter published on X ahead of planned renewed protests from next Tuesday, said those who had launched the movement no longer controlled it and called on students to abandon school blockades and unrest in favour of peaceful forms of protest.

"It is time to return to peaceful forms of action," Faure wrote, saying parents also had a responsibility to steer their children away from what he described as the influence of "professional rioters" and their supporters.

Student unions have called for a national day of demonstrations on Tuesday. Security officials fear that an organised protest in central Paris in particular could see further violence amid concerns that far-left anarchist groups could hijack the movement.

The students blockading high schools have voiced anger over overcrowding in classrooms, regular shortages of teachers and dilapidated buildings, blaming years of underinvestment.