French police arrested a man on Sunday evening after he deliberately mowed down a dozen pedestrians in the eastern city of Dijon, badly injuring two of them and shouting "Allahu Akbar" ("God is the greatest"), authorities said.

The previous day, French police in central France shot dead a man who stabbed and wounded three officers in a police station while shouting those same Arabic words.

The Dijon driver, in his forties, slammed his car into groups of pedestrians in five parts of the city before he was arrested and held for questioning, a spokesman for the Interior ministry said on BFM TV.

Eleven people were injured, two of them seriously, but their lives were not at risk, local authorities said.

According to testimonies on the scene, the driver also invoked "the children of Palestine" to explain his actions, the ministry's spokesman said.

He added that investigators had yet to determine what his motives were and whether he suffered from mental illness.

France is on high alert for attacks from Islamist extremists on its soil following calls from Islamic State (IS) militants to target countries taking part in the U.S.-led coalition bombing IS positions in Iraq.