The satirical magazine Charlie Hebdo has reportedly received death threats warning of an "imminent" attack after it published a controversial cover depicting a Muslim man and woman running down a beach half naked.

The latest issue, published last Wednesday, shows on its front page a bearded man and a woman in a hijab with the caption: 'The reform of Islam: Muslims loosen up'.

The cover refers to the ban on 'burkini' swimsuits in Cannes on France's south coast following the lorry attack on Nice on 14 July. The town of Villeneuve-Loubet and a Corsican seaside resort have since also banned the Muslim beach dress.

Charlie Hebdo was targeted by Islamist gunmen on 7 January 2015, when 12 people were shot dead in its newsroom. Al Qaida in the Arabian Peninsula claimed responsibility for the attack, saying that it was in revenge for the paper's depiction of the Prophet Mohammed.

Le Parisien reported that the magazine has now received a further death threat via its Facebook page.

The Paris prosecutor's office has reportedly begun an investigation into the threat. A spokeswoman for the office, Agnes Thibault-Lecuivre, said that the investigation for "written death threats" follows around a dozen postings in July and August on the paper's Facebook page.

A separate investigation was carried out in June for similar threats.

The Socialist mayor Ange-Pierre Vivoni of Sisco, on the French Mediterranean island of Corsica, told BFM Television the burkini was not acceptable in his town, following the ban in Cannes and Villeneuve-Loubet. "People here feel provoked by things like that," he said.

Vivoni said that he was not targeting Muslims generally but instead wanted to get rid of Islamist fundamentalists on the island. "These people have no business here," he said.

The latest ban follows a scuffle on the Sisco beach on Saturday night. Vivoni denied reports that the row had been sparked by a tourist taking pictures of Muslim women bathing in a burkini.

"The brawl was not due to a burkini," he said. "Young Corsicans were defending tourists who were peacefully taking pictures of the landscape."

He added: "The population of Sisco lives in permanent fear. There are many provocateurs here ...We are living on a powder keg."