Demonstrators on the Place de la Republique held aloft posters declaring: "No to totalitarianism of thought" and "I am a teacher" in memory of murdered colleague Samuel Paty.

"You do not scare us. We are not afraid. You will not divide us. We are France!" tweeted Prime Minister Jean Castex, who joined the Paris demonstration.

Castex was accompanied by Education Minister Jean-Michel Blanquer, Paris mayor Anne Hidalgo and junior interior minister Marlene Schiappa who said she was there "in support of teachers, of secularism, of freedom of expression". Politicians from the other major parties also attended.

Some in the crowd chanted "I am Samuel", echoing the "I am Charlie" cry that travelled around the world after Islamist gunmen killed 12 people at the Charlie Hebdo satirical magazine in 2015 for publishing caricatures of the Islamic prophet.

Between bursts of applause, others recited: "Freedom of expression, freedom to teach."

"I am here as a teacher, as a mother, as a Frenchwoman and as a republican," said participant Virginie.

The Charlie Hebdo attack in 2015 unleashed a wave of Islamist violence and forced France into a national discussion about Islam's place in a secular society.

After the massacre at the magazine, some 1.5 million people gathered on the same Place de la Republique in support of freedom of expression.

Local authorities said around 12,000 people rallied in Lyon in eastern France.

In Toulouse, in the southwest, around 5,000 turned out. "The entire educational community is affected, and beyond it society as a whole," teachers union representative Bernard Deswarte said there.

Hundreds more assembled in Nice on the south coast, where in 2016 a man killed 86 people when he rammed a truck into a crowd on the July 14 national holiday.

"Everyone is in danger today," said student Valentine Mule, 18, attending the Nice rally. "Things have to change."

More than 3,000 marched in the eastern city of Strasboug, 1,500 at Lille, in the north, and in the south, 2,500 in Marseille and 2,000 in Montpellier.

Samuel Paty was murdered on his way home from the school where he taught in a suburb northwest of Paris on Friday afternoon.

A photo of the teacher and a message confessing to his murder was found on the mobile phone of his killer, 18-year-old Chechen Abdullakh Anzorov, who was shot dead by police.

Witnesses said the suspect was spotted at the school on Friday asking pupils where he could find Paty.

On Saturday, anti-terror prosecutor Jean-Francois Ricard said Paty had been the target of online threats for showing the cartoons to his civics class.

Depictions of the prophet are widely regarded as taboo in Islam.

The father of one schoolgirl had launched an online call for "mobilisation" against the teacher and had sought his dismissal from the school.

The aggrieved father had named Paty and given the school's address in a social media post just days before the beheading, which President Emmanuel Macron has labelled an Islamist terror attack.

The father and a known Islamist militant who was involved in his campaign against Paty are among those arrested, along with four members of Anzorov's family.

An 11th person was taken into custody on Sunday, a judicial source said, without providing details.

Ricard did not say if the assailant had any links to the school or had acted independently in response to the online campaign.

The Russian embassy in Paris said Anzorov's family arrived in France from Chechnya when he was six to seek asylum.

Locals in the Normandy town of Evreux where the attacker lived described him as low key, saying he got into fights as a child but had calmed down as he became increasingly religious in recent years.

Friday's attack was the second of its kind since a trial started last month over the Charlie Hebdo killings.

The magazine republished the controversial cartoons in the run-up to the trial, and last month a young Pakistani man wounded two people with a meat cleaver outside Charlie Hebdo's former office.

On Saturday, hundreds of pupils, teachers, parents and well-wishers flocked to Paty's school to lay white roses.

"For the first time, a teacher was attacked for what he teaches," said a colleague from a neighbouring town who gave only his first name, Lionel.

Kamel Kabtane, rector of the mosque of Lyon and a senior Muslim figure, told AFP on Sunday that Paty was merely been "doing his job" and had been "respectful" in doing so.

Ministers who form France's defence council met on Sunday to discuss the Islamist threat.

A national tribute is to be held for Paty on Wednesday.