The mayor of the south-western town of Leucate, Michel Py, on Tuesday announced his intention to sign a decree barring access to public beaches to "any person who is not properly dressed, respectful of moral behaviour and secularism, hygiene and bathing safety".
Olivier Majewicz, the mayor of the Channel town of Oye-Plage, said he would ban the burkini after seeing a woman wearing "a complete cape and gloves, covering her face and her eyes" heading for the beach on Sunday, while the mayor of nearby Le Touquet, Daniel Fasquelle, said he would follow suit in the coming days "to fight against religious proselytising".
"There are no burkinis in Le Touquet at the moment but I don't want the town hall to be caught off guard if we are affected by this phenomenon," he told the AFP news agency.
The southern French resorts of Cannes and Villeneuve-Loubet and the Corsican village of Sisco have already banned the garment and three women have already been fined 38 euros each for wearing it, while another six agreed to leave a beach after being "called to order", according to Le Parisien-Aujourd'hui en France newspaper.
Valls backs mayors
Valls told the regional newspaper La Provence that he "understands" the mayors as long as they are "motivated by the will to encourage people to live together rather than by political agendas".
"Beaches, like all public spaces, must be kept free of religious claims," he said, but he added that he had no plans to propose a law at national level on the question.
Valls's statement drew an angry reaction from Communist Party spokesperson Olivier Dartigolles.
"Hasn't he got anything better to do, our country's prime minister?" he declared on France Info radio.
"In a way he's playing the terrorists' game since that's exactly what the terrorists want in the end, a war of religion, permanent tensions, a movement towards civil war."
Italian minister critices burkini ban
Italian Interior Minister Angelino Alfano described the burkini ban as "inappropriate, if not dangerous" in an interview with the Corriere della Sera newspaper Wednesday, adding that the "French model does not seem to be working very well".
The move is a "potential provocation that could attract terror attacks", he said.
Italy will step up monitoring of mosques and training of imams to fight Islamist extremism, he said.
To read our coverage of France's burka ban click here
To read our coverage of last year's Paris attacks click here