PARIS - The Knife-wielding man who on Thursday attacked worshipers at a church in the French city of Nice was a Tunisian national who entered France from Italy in early October, France's anti-terrorism prosecutor Jean-Francois Ricard said at a press conference.

According to the first indications, the assailant was carrying an Italian Red Cross document identifying him as a Tunisian national born in 1999.

"Investigation showed that this identity is indeed that of the perpetrator," said Ricard.

Not known to police and intelligence services, he landed in Italy's southern Mediterranean island of Lampedusa on Sept 20 and entered France on Oct 9. An investigation is underway to determine the motive and to establish whether the attacker acted alone or have been guided, he added.

On Thursday morning, the attacker armed with three knives entered Notre-Dame basilica in central Nice. He killed a 55-year-old sexton and a 60-year-old woman, seriously injuring another female worshiper, Ricard said.

The 44-year-old woman who managed to escape to a nearby restaurant succumbed to her injuries a few minutes later, he added.

Shortly after the attack, the knifeman was shot and seriously wounded by police. He was hospitalized and remained in critical condition, according to the prosecutor.

The attacker "kept repeating in front of us "Allah Akhbar" (God is the Greatest) while he was medicalized," Christian Estrosi, Mayor of Nice, told reporters on the spot earlier in the day.

"Many investigations are still underway, in particular, to determine the course of the murderous journey as well as all the elements related to it," said the prosecutor.

Speaking to reporters from the attack's scene, President Emmanuel Macron denounced the "Islamist terrorist attack", pledging an "absolute firmness" to cope with the terrorist threat.

"It's very clear that it is France which is under attack," Macron said.

Within hours of the Nice attack, a man had reportedly threatened passersby with a handgun in Montfavet, near the southern French city of Avignon, before being shot dead by police, local broadcaster Europe 1 reported.

France has been on high alert after a knife attack near the former office in central Paris of the satirical magazine Charlie Hebdo on Sept 25 and the beheading of a history teacher outside a middle school in Paris suburbs on Oct 16.

Following Thursday's assault, the country has raised its security threat level to the highest "to adapt to the terrorist threat". Additional 4,000 security forces would be deployed across the country to ensure the security notably of places of worship and schools, Macron said.

"We will not give any ground," said the president. "In France, there is only one community, it is the national community... We must in these moments unite and not give in to the spirit of division."

He pledged to enact further actions to fight terrorism during a defense council on Friday morning.