PARIS (AFP) - A driver shouted "Allahu Akbar" ("God is greatest") as he ploughed into groups of people in the eastern French city of Dijon on Sunday injuring 11 people, two seriously, a source close to the investigation said.

"The man, born in 1974, is apparently imbalanced and had been in a psychiatric hospital," the source said, adding that "for now his motives are still unclear".

The attack came the day after a French convert to Islam was shot dead after attacking three police officers with a knife while also reportedly crying "Allahu Akbar" in the central town of Joue-les-Tours.

The driver in Dijon was arrested by police after targeting passersby at five different places in the city on Sunday evening, a police source said.

"Nine people were lightly injured and two others seriously but their lives do not appear to be in danger," the source added.

Witnesses told police that the driver shouted "Allahu Akbar" and "that he was acting for the children of Palestine," a source close to the investigation said.

Interior Minister Bernard Cazeneuve told French television station TF1 on Sunday that the man who was shot dead the day before after attacking a police station in Joue-Les-Tours was "very unstable".

The anti-terror branch of the Paris prosecutor's office has opened a probe into that attack, with the line of inquiry focusing on an attack motivated by radical Islam.