The French government has stepped up security across the country after a man shouting "Allahu Akbar" (God is great) rammed his car into crowds of people in Dijon, in the second incident in as many days to raise fears of Islamist terrorist attacks.

The 40-year-old driver injured 11 people, two seriously, by ploughing a black Renault Clio into pedestrians at several different locations in the eastern France city on Sunday evening.

Police said that motives for the attack were not immediately clear. The driver has been arrested and some witnesses told local media he was also heard shouting that he was "acting for the children of Palestine".

"The man, born in 1974, is apparently unbalanced and had been in a psychiatric hospital," a police source close to the investigation told AFP.

Prime Minister Manuel Valls tweeted his solidarity to the victims and support to their families.

The rampage came a day after a knife-wielding man also shouting "Allahu Akbar" stabbed three officers in a police station in the central town of Joue-les-Tours.

The 20-year-old attacker, a Muslim convert identified as Bertrand Nzohabonayo, was killed after slashing the throat of an officer and wounding two others. The incident is being investigated by anti-terror police.

French government response

The government has since stepped up security measures for police and other authorities fearing more possible "lone wolf" attacks.

Interior Ministry spokesman Pierre-Henry Brandet said it was too early to say whether there was any connection between the incidents in Dijon and Joue-les-Tours.

Visiting Joue-les-Tours, interior minister Bernard Cazeneuve said authorities have foiled five terrorist attacks planned by Islamist radicals in the country since 2013.

Cazeneuve said that more than 1,200 people living in France are involved in jihadist networks, adding that the number has doubled in the last 12 months, Le Figaro reported.

France, which is home to Europe's largest Muslim population, has been directly touched by the rise of Islamist groups in the Middle East, with the Islamic State and other terrorist organizations repeatedly calling for attacks against the country.

In 2012, four Jews - including three children - and three soldiers were shot dead in Toulouse by 23-year-old radical Mohamed Merah.

Earlier in 2014, Mehdi Nemmouche, a 29-year-old of Franco-Algerian origin, shot four people dead at the Brussels Jewish Museum in Belgium.

About 1,000 French citizens are believed to have travelled to Syria to join jihadist militias.