A woman was beheaded by an attacker with a knife who also killed two other people at a church in the French city of Nice on Thursday, police said, in an incident the city's mayor described as terrorism.

Mayor Christian Estrosi said on Twitter the knife attack had happened in or near the city's Notre Dame church and that police had detained the attacker.

Police said three people were confirmed to have died in the attack and several were injured.

A police source said a woman was decapitated. French politician Marine Le Pen also spoke of a decapitation having occurred in the attack.

The French anti-terrorist prosecutor's department said it had been asked to investigate the attack.

Reuters journalists at the scene said police armed with automatic weapons had put up a security cordon around the church, which is on Nice's Jean Medecin avenue, the city's main shopping thoroughfare. Ambulances and fire service vehicles were also at the scene.

The attack comes while France is still reeling from the beheading earlier this month of French middle school teacher Samuel Paty in Paris by a man of Chechen origin.

The attacker had said he wanted to punish Paty for showing pupils cartoons of the Prophet Mohammad in a civics lesson.

It was not immediately clear what the motive was for the Nice attack, or if there was any connection to the cartoons, which Muslims consider to be blasphemous.

Since Paty's killing, French officials - backed by many ordinary citizens - have re-asserted the right to display the cartoons, and the images have been widely displayed at marches in solidarity with the killed teacher.

That has prompted an outpouring of anger in parts of the Muslim world, with some governments accusing French leader Emmanuel Macron of pursuing an anti-Islam agenda.