The assailant was shot by police and later died of his injuries.
The man suspected of beheading a French teacher who had shown pupils cartoons of the prophet Muhammed was an 18-year-old from Chechnya, a judicial source said.
Five more people have been detained over the murder on Friday outside Paris, including the parents of a child at the school where the teacher was working, bringing to nine the total number currently under arrest, said the source on Saturday, who asked not to be named.
According to the source, the two detained parents had signalled their disagreement with the teacher's decision to show the cartoons.
The other new people detained for questioning are members of the suspect's social circle but not family members.
The assailant was shot by police and later died of his injuries. Identification documents were found on him.
France has seen a wave of terror attacks since the 2015 terror attacks on the satirical magazine Charlie Hebdo and a Jewish supermarket in the capital.
French anti-terror prosecutors said they were treating the assault as "a murder linked to a terrorist organisation".
The attack happened on the outskirts of Paris at around 1500GMT near the middle school where the teacher worked in Conflans Saint-Honorine, a northwestern suburb around 30 kilometres from the city centre.
The killing bore the hallmarks of "a terrorist attack", President Emmanuel Macron said as he visited the scene.
Cartoon parody of Prophet
The middle school teacher was decapitated on the street of a Paris suburb showed his teenage students a cartoon lampooning the Prophet Muhammad as part of a class on freedom of expression earlier this month, parents said.
Nordine Chaouadi told Reuters he was the father of a 13-year-old pupil who attended the civics class given by the teacher, whom parents gathered outside the college referred to as Mr Paty.
French media have identified him as Samuel Paty.
The teacher had asked pupils who were Muslim to raise their hands and invited them to leave, advising them he would be showing a caricature of Mohammad that might cause offence, said Chaouadi.
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