The Tunisian man accused of a gruesome terror attack in a church in the French city of Nice was not listed as a suspected militant by that country’s police.

Tunisia’s counter-militancy court spokesman Mohsen Dali said officials there knew only that Brahim Aouissaoui left the country on September 14 by boat.

He said Tunisia had begun its own forensic investigation into Aouissaoui, a 21-year-old who has been named by Tunisian security sources and French police as the suspect involved in Thursday’s knife attack at the Notre-Dame basilica in the southern French city.

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According to reports, Aouissaoui shouted “Allahu Akbar” (God is Greatest) before beheading a woman and killing two other people in the church. He was shot and taken away by police, and reportedly remains in hospital in a critical condition.

Chief anti-terrorist prosecutor Jean-Francois Ricard said the suspect was a 1999-born Tunisian who arrived in Lampedusa, the Italian island off Tunisia that is the main landing point for migrants from Africa, on September 20.

Mr Ricard said the man entered Nice by train early on Thursday and made his way to the church, where he stabbed and killed the 55-year-old sexton and beheaded a 60-year-old woman.

He also stabbed a 44-year-old woman. She managed to flee to a nearby cafe, where she raised the alarm before dying.

Another witness also reportedly alerted authorities using 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.”

Police arrived and confronted the attacker, who was still shouting “Allahu Akbar”. They shot and wounded him.

“On the attacker we found a Koran and two telephones, the knife of the crime – 30 centimetres with a cutting edge of 17 centimetres,” Mr Ricard said.

“We also found a bag left by the attacker. Next to this bag were two knives that were not used in the attack.”

Forensice officers in front of the Nice church after Thursday’s attack. Photo: Getty

French President Emmanuel Macron called it an “Islamist attack” and said France would deploy thousands more soldiers to protect important sites such as places of worship and schools, while the country’s security alert has been raised to its highest level.

Speaking outside the church on Thursday, Mr Macron said France had been attacked “over our values, for our taste for freedom, for the ability on our soil to have freedom of belief.

“I say it with great clarity again today: We will not give any ground.”

The attack came just under two weeks after a middle-school teacher in a Paris suburb was beheaded by an 18-year-old attacker apparently incensed by the teacher showing a cartoon of the Prophet Mohammad in class.

Thursday’s attacks, on the birthday of the Prophet Mohammad, came at a time of growing Muslim anger at the defence of the right to publish cartoons and protesters have denounced France in rallies in several Muslim-majority countries.

There were also two other attacks on Thursday, one in France and one in Saudi Arabia.

A man was shot dead in Montfavet, near the southern French city of Avignon, after threatening police with a handgun.

In Jeddah, Saudi Arabia, a guard was attacked outside the French consulate. A suspect was arrested and the guard taken to hospital.

Back in Nice, police armed with automatic weapons set up a security cordon around the church, which is on the city’s Avenue Jean Medecin, the French Riviera city’s main shopping thoroughfare.

US President Donald Trump said America “stands with our oldest Ally in this fight.

“These Radical Islamic terrorist attacks must stop immediately,” he tweeted. “No country, France or otherwise can long put up with it!”

Condemnations of the attack also came from Britain, the Netherlands, Italy, Spain, Saudi Arabia and Turkey, whose President Tayyip Erdogan this week slammed France over displays of the Prophet Mohammad.

-with AAP