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Three people are believed to have been killed and several others injured after a knife attack near to the Notre Dame church.
The city's mayor Christian Estrosi tweeted: "Everything suggests a terrorist attack."
He also confirmed that a person had been arrested.
Estrosi went on to say that the city of Nice had 'paid too heavy a price in the same way as our country in recent years.'
The French Interior Minister Gerald Darmanin confirmed that a police operation is underway, and asked members of the public to avoid the area.
The Police Nationale reiterated the calls for the public to avoid the area and to stay calm. They also confirmed that the situation was 'very serious' and that the bomb disposal squad had carried out a controlled explosion near the scene.
President Emmanuel Macron is due to visit the city later on today. He has already discussed the situation with Mayor Estrosi and Interior Minister Darmanin.
The investigation will be undertaken by the national anti-terrorist department alongside the judicial police and internal security teams.
According to reports from Associated Press, the assailant was arrested after the attack at around 9am on Thursday morning and taken to a hospital for treatment of injuries sustained in his arrest.
The suspect is believed to have been acting alone.
The French National Assembly held a minute's silence in memory of those who lost their lives after suspending a debate on the new coronavirus restrictions that will see France enter a second national lockdown this evening.
The French Prime Minister Jean Castex called for togetherness and said: "Without question this is a very serious new challenge that is striking our country,"
France is currently on a high alert for terrorist attacks.
Nice was the target of another terrorist attack on 14 July four years ago when a 31-year-old Tunisian man drove a truck through crowds celebrating Bastille Day on the streets.
86 people were killed.
Earlier this month, middle school teacher Samuel Paty was beheaded in Paris by an attacker who said he wanted to punish him for showing pupils a cartoon of the Prophet Muhammad during a lesson.
Muslims consider showing any depiction of the prophet to be blasphemous.
However, it is not yet clear what the motivation for this latest attack is.
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