France has lifted its security alert status to the highest level after a knife-wielding attacker shouting “Allahu Akbar” killed three people in a church in the city of Nice.

A defiant President Emmanuel Macron, declaring that France had been subject to an Islamist terrorist attack, said he would deploy thousands more soldiers to protect important French sites, such as places of worship and schools.

Speaking from the scene, he 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 lots of clarity again today: We will not give any ground.”

France’s chief anti-terror prosecutor Jean-François Ricard said the attacker was a Tunisian national, born in 1999, who had recently entered France from Italy.

A Tunisian security source and a French police source told Reuters the suspect’s name was Brahim Aouissaoui.

Mr Ricard said one of the women had her throat cut. A police source earlier told Reuters that the victim had been beheaded. France’s Le Monde newspaper called it an “attempted” beheading.

Mr Ricard said the attacker arrived in Italy by reaching the Mediterranean island of Lampedusa on September 20. He travelled to Paris on October 9.

The travel information came from an Italian Red Cross document found on the attacker, he said.

The Associated Press quoted Italian media reports as saying the attacker spent two weeks in quarantine on a ship off the eastern coastal town of Bari in September, before being expelled from Italy and heading to Paris.

Tunisia’s anti-terrorism court prosecutor began a forensic investigation into “the suspicion that a Tunisian committed a terrorist operation abroad”, Mohsen Dali, spokesman for the specialised counter-militancy court, said in Tunis.

The latest horrific attack on the birthday of the Prophet Mohammed came less than a fortnight after the beheading of school teacher Samuel Paty, who had used cartoons of the Muslim prophet in a civics class.

With Europe’s largest Muslim community, France has suffered a string of jihadist attacks in recent years, including bombings and shootings in Paris in 2015 that killed 130 people and a 2016 attack in Nice in which a militant drove a truck through a seafront crowd celebrating Bastille Day, killing 86.

Within hours of the Nice attack, French police killed a man who had threatened passers with a handgun in Montfavet, near the southern city of Avignon, about 270 kilometres west of Nice.

France’s Le Figaro newspaper quoted a prosecution source as saying the man had been undergoing psychiatric treatment, and that they did not believe there was a terrorism motive.

Meanwhile, in Saudi Arabia, local police said a man was arrested in the city of Jeddah after attacking and injuring a guard at the French consulate.

The French embassy said the consulate was subject to an “attack by knife which targeted a guard”, adding the guard was taken to hospital and his life was not in danger.

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World leaders have condemned the attack, with Australia’s Prime Minister Scott Morrison describing it as disgusting and cowardly.

“These multiple attacks are despicable. They are disgraceful,” he said on Friday.

“Not only are they an attack on the individuals and their families but they are an attack on liberty. When we think of France we think of liberty. And we stand with the people of France.”

Mr Morrison exchanged text messages with French President Emmanuel Macron overnight.

Mr Macron responded: “We will win.”

“We stand with France in that declaration,” the PM said.

“Free people all around the world will stand together to defend freedom, to defend our liberties and to stand against the evil terror that seeks to assault that.”

Opposition Leader Anthony Albanese said all Australians stood with France after the attack.

“This is a horrific act of terrorism that is simply barbaric and deserves to be utterly condemned,” he said.

“It will produce a real shockwave through France. It won’t blunt the French values of liberty, equality and fraternity and all Australians stand with the French people today.”

ASIO director-general Mike Burgess told a parliamentary committee he was horrified by the latest act of calculated, premeditated murder in France.

“Attacks such as this, targeting some of society’s most innocent, causes my officers at all levels, both here in Australia and overseas, to redouble our focus and our effort to counter this menacing threat,” he said.

-with agencies