Tens of thousands of people have joined rallies across France in support of protesting high school students, boosting a movement that is posing a major challenge to President Emmanuel Macron as his term in office winds down.

Some 161,500 people turned out on Tuesday according to the Interior Ministry, more than double the 71,500 it reported for Thursday’s nationwide demonstrations.

Unions helping to organise the rallies put the countrywide turnout at 480,000.

Although most of Tuesday’s demonstrations were peaceful, violence broke out on the sidelines of one of two marches in Paris, where the Interior Ministry said 41,500 people took part.

Thousands also marched in the cities of Nantes, Lyon, Lens, Strasbourg, Toulouse, Bordeaux and Marseille, according to police.

The student movement sprang up last month, with students blocking the entrances to many schools to demand better classroom conditions.

What many see as a heavy-handed police response to the students prompted more people to join Tuesday’s demonstrations.

Police have opened investigations into 34 allegations of violence against demonstrators.

Some 147 teaching staff have been injured in the protests, the Education Ministry said.

On Monday, Macron urged restraint from protesters, saying the issues “deserve time, consultations, discussion and respect”.