Four-hundred-and-forty people, mostly minors, have been arrested and 76 injured as a wave of school protests over overcrowded classes and teacher shortages spreads across France, officials say.

The demonstrations began in Paris last week but have escalated to cities including Dijon, Lyon, Strasbourg, Lille and Marseille, with teenagers blockading their schools for days.

Education Minister Édouard Geffray said while some of the students’ demands were legitimate what worried him was the violence.

He spoke of one young man having lost the use of part of his hand after firing a mortar firework. The dozens hurt since the start of protests included both pupils and staff, he said.

Secondary school students’ union USL says as many as 400 of France’s 3,700 lycées for 15-18 year-olds have been blockaded and it has called for further action on Thursday, including at universities.

Firefighters were called out in Strasbourg after bins were set alight outside a school, while in Dijon police used tear gas to disperse dozens of students, French media reported on Wednesday.

On Tuesday alone, at least 10 teachers and several students were hurt, according to the education minister, who added that one teacher had been beaten up.

Geffray singled out the radical left party La France Insoumise (LFI – France Unbowed) for stirring up trouble.

The LFI mayor of northern Paris suburb Seine-Saint-Denis, Bally Bagayoko, who has praised the protesters, has been criticised for suggesting that in some cases “violence can be legitimate” when a teenager is faced with riot police firing so-called “flashballs”.

“Every time we try to express ourselves we get tear-gassed, they don’t try to understand us,” students at the Paul-Éluard lycée in Saint-Denis told France Inter radio. “When we try to talk about our rights, they tear-gas us, they hit us.”

For days students have blockaded the lycée in Saint-Denis, and part of the school gate has been torn down.

Bagayoko was pictured on Monday dancing with protesting students outside the school and singing the Marseillaise with them, prompting Valérie Pécresse, the conservative head of the Île-de-France region that includes Paris, to demand he pays for some of the damage.