French police have shot dead an armed man who allegedly set fire to a synagogue in the northwestern city of Rouen, officials said.

Interior Minister Gerald Darmanin posted on X that the armed man was “neutralized.”

“In Rouen, national police officers neutralised early this morning an armed individual clearly wanting to set fire to the city’s synagogue. I congratulate them for their reactivity and their courage,” he said.

The synagogue is said to have suffered significant damage in the attack.

Local police responded at 6:45am to reports of a fire rising from the main Rouen synagogue.

The suspect exited the synagogue threatening police with a knife and an iron bar, according to the national police information service. An officer opened fire and fatally wounded the man, police said.

A source told Agence France-Presse the man “was armed with a knife and an iron bar, he approached police, who fired”.

The Rouen synagogue sustained significant damage, including to its furniture, but no one was injured, mayor Nicolas Mayer-Rossignol said.

Mayer-Rossignol added that the town was "battered and shocked".

"An armed man somehow climbed up the synagogue and threw an object, a sort of molotov cocktail, into the main praying room," the mayor told reporters.

“When the Jewish community is attacked, it’s an attack on the national community, an attack on France, an attack on all French citizens,” he said.

“It’s a fright for the whole nation,” he added.

The fire has been brought under control, according to officials, but the attacker's identity and motive are still unclear.

Two separate investigations have been opened, one into the synagogue fire and another into the circumstances of the death of the suspected killed by the police, Rouen authorities said on Friday morning.

"It's once again an attempt to impose a climate of terror on the Jews of our country," Yonathan Arfi, president of the CRIF Jewish advocacy group, tweeted in response to the incident.

The chief rabbi of France, Haïm Korsia, tweeted his thanks to the police and the town’s mayor, and said, “I spoke at length with the president of the community and will spend a Shabbat there very soon”.