Thousands have attended rallies across France in honour of Samuel Paty, the teacher beheaded after showing cartoons of the Prophet Muhammad to his pupils.

People in the Place de la République in Paris carried the slogan "Je suis enseignant" (I am a teacher), with PM Jean Castex saying: "We are France!"

A man named as Abdoulakh A was shot dead by police on Friday after killing Mr Paty close to his school near Paris.

An 11th person has now been arrested as part of the investigation.

No details have been given about the arrest. Four close relatives of the suspect were detained shortly after the killing. Six more people were held on Saturday, including the father of a pupil at the school and a preacher described by French media as a radical Islamist.

President Emmanuel Macron said  the attack bore all the hallmarks of an "Islamist terrorist attack" and the teacher had been murdered because he "taught freedom of expression".

The murder comes as a trial over the 2015 attack on Charlie Hebdo - a satirical magazine that has published cartoons of the Prophet Muhammad - is under way.

Where have the rallies been taking place?

The Place de la République in Paris filled with people rallying in support of Mr Paty, 47. Mr Castex and Paris Mayor Anne Hidalgo joined them.

The square was the scene of a huge demonstration in which 1.5 million people showed solidarity with Charlie Hebdo following the deadly attack of January 2015.

One protester on Sunday carried a sign reading "zero tolerance to all enemies of the Republic", another "I am a professor. I'm thinking of you, Samuel."

Another told Le Figaro she was a French Muslim who was at the rally to express her disgust at the latest killing.

A minute's silence was followed by the playing of the Marseillaise. All the protesters were wearing masks to protect from coronavirus.

Mr Castex tweeted the rendition of the anthem, along with the words "you do not scare us... we are France!"

Vous ne nous faites pas peur.
Nous n’avons pas peur.
Vous ne nous diviserez pas.
Nous sommes la France ! pic.twitter.com/GjUQo9AePa

— Jean Castex (@JeanCASTEX) October 18, 2020

Education Minister Jean-Michel Blanquer said France would succeed in defeating the enemies of democracy if it were united and that all teachers in France needed support.

Nathalie, a teacher from Chelles who was at the Paris rally, told Le Monde she was there because she had "realised you can die of teaching".

In Lille, people carried banners and placards with the simple words "I am Samuel".

Thousands of people also gathered in Place Bellecour in Lyon to pay their respects, with another large turnout in Nantes.

Demonstrations are also being held in Toulouse, Strasbourg, Marseille, Bordeaux and elsewhere.

In addition to Sunday's demonstrations, there will be a national tribute paid to Mr Paty on Wednesday.

On Saturday, Tareq Oubrou, imam of a mosque in Bordeaux, told France Inter: "A civilisation does not kill an innocent person, barbarism does."

What happened on Friday?

Anti-terrorism prosecutor Jean-François Ricard said that the suspect, who lived in the Normandy town of Évreux, about 100km (60 miles) from the murder scene, went to Mr Paty's school in Conflans-Sainte-Honorine on Friday afternoon and asked students to point out the teacher.

Abdoulakh A, an 18-year-old born in Moscow of Chechen origin, had no apparent connection with the teacher or the school.

He followed Mr Paty as he walked home from work. The suspect used a knife to attack the teacher in the head, and then beheaded him.

Witnesses are said to have heard the attacker shout "Allahu Akbar", or "God is Greatest".

As police approached him, he fired at them with an airgun. Officers returned fire, hitting him nine times. A 30cm-long (12in) blade was found close by.

Authorities said the man had been before courts but only on minor misdemeanour charges.

What's the latest in the investigation?

Mr Ricard said Mr Paty had been the target of threats since he showed the cartoons of the Prophet Muhammad during a class about freedom of speech.

As he had done in similar lessons in recent years, Mr Paty, a history and geography teacher, advised Muslim students to look away if they thought they might be offended.

A parent of one of the pupils reacted angrily, and went to the school to complain.

He and another man who accompanied him - Abdelhakim Sefrioui, a preacher and activist - made videos calling Mr Paty a "voyou" (thug) and demanding his suspension.

Mr Sefrioui has reportedly been known to French intelligence services for years. Both he and the father are now in custody.