Police sources said the unrest was sparked by an attack on a 16-year-old member of the Chechen community on June 10th.
Members of the Chechen diaspora then set out on so-called punishment raids seeking to avenge the assault, they said.
After three successive nights of violence, early Monday evening some 150 people, some hooded and armed, again assembled in Dijon, setting rubbish bins and a car on fire.
Some also shot into the air, police sources told AFP.
Videos posted on social media showed armed, hooded and masked men waving guns in the air.
One video, which source cannot be verified, showed a car at full speed crashing violently as several men ran at it.
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“What happened is unprecedented and unacceptable,” the city's mayor, Francois Rebsamen, told AFP.
Attacks had already taken place on three successive nights starting Friday, with many people wielding baseball bats.
The local prefect Bernard Schmeltz – the top state official in the region – said in a statement that the violence “appeared to be part of a settling of scores between members of the Chechen community in France and residents” of Dijon.
Police said that in one incident some 50 Chechens entered the restive district of Gresilles overnight Saturday, and a man who owns a pizzeria was badly wounded by apparent gunfire.
Even more people, around 200, also entered Gresilles late on Sunday with violent intent.
Police in Dijon on June 15th. Photo: AFP
'Also Belgium and Germany'
In an interview with local daily Le Bien Public, a man claiming to be a Chechen said the raids aimed to avenge an assault by local drug dealers on the 16-year-old.
“There were about a hundred of us from all over France but also from Belgium and Germany. We never intended to ransack the city or take it out on the people,” said the man, who was not identified by name.
Dijon prosecutor Eric Mathais said a total of six people had been injured in the three incidents on the successive nights, but no one has yet been arrested.
A probe has been opened into attempted murder by a criminal gang, he added.
Police sent in
Rebsamen said the police reinforcements were arriving after he spoke by telephone with Interior Minister Christophe Castaner.
Thirty-seven anti-riot police members came on Sunday, while 110 additional gendarmes would be deployed from Monday, he said.
Chechnya is a predominantly Muslim Russian republic in the North Caucasus.
Two wars in the 1990s triggered a wave of emigration, with many Chechens heading for western Europe.