A French nursery school teacher who claimed he was stabbed in his classroom by an Islamic State (IS) supporter has admitted to prosecutors that he invented the story.

The 45-year-old teacher at a school in Aubervilliers, north-east of Paris, was hospitalised with light stab wounds in his side and throat.

He had earlier claimed that a man in overalls and a balaclava had arrived while he was preparing his class on Monday, grabbed a box cutter and scissors that were in the room, and attacked him.

The teacher further claimed that the man shouted: "This is Daesh. This is a warning."

Daesh is another name for IS.

Prosecutors said they were still questioning the teacher, whose injuries were not considered life-threatening, over why he lied.

With France on edge a month on from attacks in Paris, and with the IS calling for attacks on French schools, the investigation had been immediately taken over by anti-terrorism prosecutors.

The case even prompted a visit by Education Minister Najat Vallaud-Belkacem, who vowed to boost security at France's schools.

The Islamic State's French-language magazine Dar-al-Islam called in its November edition for its followers to kill teachers in the French education system, describing them as "enemies of Allah".

"This education, in the case of France in particular, is a means of propaganda used to impose the corrupt way of thought established by the Judeo-masonry," it said.

"Muslims must know the French education system is built against religion and Islam as the only religion of truth cannot cohabit with this fanatic secularism."

Last month's attacks by IS in Paris left 130 dead and saw France impose a three-month state of emergency.

"We will continue to reinforce security measures at schools in a context where schools feel threatened," said Vallaud-Belkacem on Monday.

Rachel Schneider of the main primary school teachers' union SNUipp said the IS threats had alarmed faculty members.

"We have received many calls from colleagues, who are very worried. They don't necessarily think there will be an organised attack, but they fear this message of murderous madness will inspire unstable people to action," she said.

In March 2012, jihadist Mohamed Merah killed three children and a teacher outside a Jewish school in south-western France in attacks which also saw him kill three soldiers.

AFP