Police operations are under way into dozens of people who allegedly issued messages of support for the attacker after the beheading of a history teacher near Paris, the French interior minister has said.
Gerald Darmanin told radio station Europe 1 that at least 80 cases of hate speech have been reported since Friday’s attack.
Samuel Paty was beheaded in Conflans-Sainte-Honorine, north-west of Paris, by an 18-year-old Moscow-born Chechen refugee, who was later shot dead by police.
Police officials said Mr Paty had discussed caricatures of Islam’s Prophet Mohammed with his class, leading to threats.
French President Emmanuel Macron held a defence council on Sunday at the Elysee presidential palace and the government will reinforce security at schools when classes resume on November 2 after two weeks of holidays, Mr Macron’s office said.
A national homage is to be held for Mr Paty on Wednesday.
Thousands of demonstrators gathered on Sunday across France in support of freedom of speech and in memory of Mr Paty.
French authorities said they detained 11 people following the killing.
Mr Darmanin said they include the father of a student and an Islamist activist who both “obviously launched a fatwa” against the teacher.
Mr Darmanin said authorities were also looking into about 50 associations suspected of encouraging hate speech, adding that some will be dissolved.
The president of the Conference of Imams in France, Hassen Chalghoumi, told French news broadcaster BFM TV: “We are hurt, we are condemning this barbaric act,” adding “Samuel is a martyr of freedom”.
Mr Chalghoumi, who is an imam in Drancy, a suburb north-east of Paris, said he had received death threats and insults on social media from radical Islamists in recent days.
Justice authorities opened an investigation for murder with a suspected terrorist motive.
At least four of those detained are family members of the attacker, who had been granted 10-year residency in France as a refugee in March.
He was armed with a knife and an airsoft gun, which fires plastic pellets.
Anti-terrorism prosecutor Jean-Francois Ricard said a text claiming responsibility and a photograph of the victim were found on the attacker’s phone.