RAMBOUILLET, (France): French prosecutors opened a terror inquiry Friday after a police employee was stabbed to death at a station southwest of Paris by a suspected extremist from Tunisia who was then shot dead by the security forces.

President Emmanuel Macron said France would never give in to "Islamist terrorism" after the attack in Rambouillet, a tranquil commuter town about 60 kilometres (40 miles) from Paris, which revived the trauma of a spate of deadly attacks last year.

France's national anti-terrorism prosecutors said they had opened a terror investigation, also involving the DGSI domestic intelligence service, into the murder of a person holding public authority.

A source close to the inquiry told AFP the attacker shouted "Allahu Akbar" (God is Greatest) during the attack.

Chief anti-terror prosecutor Jean-Francois Ricard, who spoke outside the station along with Prime Minister Jean Castex, confirmed that "comments made by the assailant" indicated a terror motive, without further details.

The attack took place in the secure entrance area of the station at around 2:20 pm (1220 GMT), a police source added, asking not to be named.

The 49-year-old woman, an administrative assistant and mother of two who was returning from a lunch break, was stabbed in the throat twice and died of her wounds shortly afterwards, the source said.

The attacker, 36, was fatally wounded when an officer opened fire on him.

He arrived in France illegally in 2009 but had since obtained residency papers, a police source said, adding that he was unknown to security services. He had just moved to Rambouillet.

Macron vowed on Twitter that "in our fight against Islamist terrorism, we will never give in," identifying the murdered woman as Stephanie.

"The nation is by the side of her family, her colleagues and security forces," he said.

Interior Minister Gerald Darmanin, who also visited officers in Rambouillet, said security would be stepped up at stations nationwide.