Three people have been killed in a knife attack at a church in the French city of Nice.
Nice Mayor Christian Estrosi said there had been a "terrorist attack at the heart of the Notre-Dame basilica".
One elderly victim who had come to pray was "virtually beheaded". A suspect was shot and detained shortly afterwards.
Mr Estrosi spoke of "Islamo-fascism" and that the suspect had "repeated endlessly 'Allahu Akbar' (God is greatest)."
President Emmanuel Macron is on his way to the scene. France's national anti-terror prosecutors have opened a murder inquiry.
Mr Estrosi compared the attack to the recent murder of teacher Samuel Paty, who was beheaded close to his school outside Paris earlier this month.
Police have not suggested a motive for the attack in Nice. However, it follows days of protests in some Muslim-majority countries triggered by President Macron's defence of French cartoons that depict the Prophet Mohammed. There have been calls in some countries for a boycott of French goods.
Meanwhile, two further attacks took place on Thursday morning, one in France and one in Saudi Arabia.
A man was shot dead in Montfavet near Avignon after threatening police with a handgun. And a guard was attacked outside the French consulate in Jeddah. A suspect was arrested and the guard taken to hospital.
What is known about the attack in Nice?
Two of those who died were attacked inside the church, the elderly woman and a man who was found with his throat cut, reports said.
A woman managed to flee to a nearby cafe after being stabbed several times, but died later.
It later emerged that a witness had managed to raise the alarm with a special protection system set up by the city.
Chloe, a witness who lives near the church, told the BBC: "We heard many people shouting in the street. We saw from the window that there were many, many policemen coming, and gunshots, many gunshots."
Tom Vannier, a journalism student who arrived at the scene just after the attack, told the BBC that people were crying on the street.
Four years ago Nice was the scene of another terror attack when a man drove a truck into seaside crowds, killing 86 people.
The terrorist threat level in France is as high now as it was in 2015-16, the terrible days of Charlie-Hebdo, Bataclan, the Nice lorry-killer and the murder of Father Hamel in his church in Rouen. Things were bad enough then - and many more people died in those attacks. So why does this outbreak of Islamist violence feel somehow more scary?
One reason must be the symbolism of the Samuel Paty beheading. That a simple history teacher could be murdered - and not randomly but actually selected for murder - has been deeply unsettling for French people. Likewise the targeting today of Christian worshippers in Nice.
But it is also the context: the instant logic of action-response that followed President Macron's robust defence of secularism at Samuel Paty's memorial 10 days ago. All it took was a speech, then there were the threats, then there were the deaths.
With a new Covid lockdown providing an eerie backdrop to these events, small wonder the French are feeling disoriented and frightened.
What has the reaction been?
France's interior minister appealed to people to avoid the area in the centre of the French Riviera city. Gérald Darmanin said he was convening a crisis meeting at the ministry in Paris.
A minute's silence was held in the National Assembly, where Prime Minister Jean Castex had just been giving details of Covid-19 lockdown measures coming into force on Thursday night.
"Without question this is a very serious new challenge that is striking our country," he said, appealing for unity and cohesion.
The French Council of the Muslim Faith condemned the Nice knife attack and spoke of its solidarity with the victims and their families.
What's the context?
Nice was the target of one of France's deadliest attacks in recent years, when a 31-year-old Tunisian drove a truck into crowds celebrating Bastille Day on 14 July 2016, killing 86 people.
Days later a priest, Father Jacques Hamel, had his throat cut during morning Mass at a church in Rouen.
Thursday's attack has echoes of another attack earlier this month near a school north-west of Paris. Samuel Paty, who was a teacher in Conflans-Sainte-Honorine, was beheaded days after showing controversial cartoons of the Prophet Muhammad to some of his pupils.
The murder has heightened tensions in France and the government's attempt to crack down on radical Islam has angered Turkey and other countries.
Turkish President Recep Tayyip Erdogan has called for a boycott of French goods.
The situation worsened after a cartoon on Mr Erdogan appeared in the satirical magazine Charlie Hebdo.