A bullet fired from an air gun crashed through a window of a Paris synagogue’s office, according to French media reports.

The rabbi and his assistant were in the David Ben Ichay Synagogue in Belleville, Paris, when the bullet was fired on Monday night.

French police reportedly are searching for two suspects who were outside the synagogue about 10 minutes before the attack, the JSSNews website reported. There were no reports of any injuries.

The latest attack comes as French Prime Minister Manuel Valls vowed to step up security nationwide following three successive, apparently unrelated bloody attacks.

While the motives behind the incidents — a knife attack on police and two car rampages onto passers-by — remain unclear, the violence has jarred nerves after repeated jihadist calls for “lone wolf” action in France over its fight against Islamic extremism.

“Fear over Christmas” titled local daily Le Parisian, while Le Figaro newspaper wrote a front-page editorial headlined “enemies from within.”

On Tuesday, Mr Valls stressed that the three incidents were “distinct”, urging the French to keep their calm and act with restraint while stressing security would be heightened.

“The number of patrols will be increased during this (Christmas) period. Two hundred to 300 soldiers will be deployed in the coming hours,” he said live on television, after holding an emergency meeting with his ministers.

The violence began on Saturday when a man reportedly shouting “Allahu Akbar” was shot dead after walking into a police station in the central town of Joue-les-Tours and attacking three officers with a knife, seriously injuring two of them.

On Sunday evening, a driver ploughed into pedestrians in Dijon in the east, injuring 13 people while shouting the same Islamic phrase which means “God Is Greater”.

On Monday night, another man rammed into a bustling Christmas market with his car in the western city of Nantes, injuring 10 people — one of whom is in critical condition — before stabbing himself repeatedly.

Mr Valls stressed there was no link between the three attacks but the ever-present threat of violence inspired by Islamic extremism has authorities concerned.

In September, the radical Islamic State group urged Muslims around the world to kill “in any manner” those from countries involved in a coalition fighting its jihadists, singling out the French.

Among instructions detailing how to kill civilians or military personnel was to “run him over with your car.”

But while the probe into Saturday’s attack is veering towards extremism — the Burundian convert to Islam who attacked police had posted an Islamic State flag on his Facebook page — the last two car rampages appear to have been committed by “unbalanced” people.

Prosecutors in charge of probing the driving incidents insisted they were not “terrorist acts”.

The assailant in Dijon had been to psychiatric hospitals 157 times, local prosecutor Marie-Christine Tarrare told reporters.

She said he told police that he ploughed into people due to a sudden “outburst of empathy for the children of Chechnya” and had shouted “Allahu Akbar” to give him courage.

Interior Minister Bernard Cazeneuve meanwhile said the attacker in Nantes also appeared to be “unbalanced” and not motivated by politics or religion.

Nevertheless, the government faced criticism it was minimising the threat, at a time when more than 1000 nationals are thought be involved in jihad on home soil, or in Syria and Iraq.

Saturday’s assailant Bertrand Nzohabonayo was not on a domestic intelligence watch-list but his brother Brice is well known for his radical views and was arrested in Burundi soon after the incident.