The mayor of Cannes first banned the burkini from the city's beaches last week, calling the swimsuit "the uniform of extremist Islamism, not of the Muslim religion" and disrespectful of "good morals and secularism".
France, which has the largest Muslim minority in Europe, estimated at 5 million, in 2010 introduced a ban on full-face niqab and burqa veils in public.
Five towns have banned them this summer and others have threatened to follow suit.
"That is not compatible with the values of France", he said in an interview with La Provence newspaper.
Since then, several other French towns have also enacted similar bans on the burkini. A minor girl who witnessed the confrontation explained the fight happened after a group of youngsters insulted tourists who were photographing women bathing in burkini. "It can not be considered only as a question of fashion or individual liberty", Rossignol said on Europe-1 radio.
Asked specifically about the burkini bans in France, he replied: "It doesn't seem to me, alas, that the French model has worked for the best".
Yet despite concerns about freedom and personal liberty for Muslim women wishing to wear the burkini, many French citizens support the bans.
Burqini's design is meant to comply with the Quranic instruction for women to dress modestly.
'What is more French than sitting on a beach in the sand?
The French government has defended municipal bans on body-covering burkini swimwear but called on mayors to try and cool tensions between communities.
While critics of the ban point out that the burkini is almost identical to a traditional wetsuit commonly worn by scuba divers and surfers. He has stated, " In France, one does not come to the beach dressed to display one's religious convictions, especially as they are false beliefs that religion does not demand". "Muslim authorities must also condemn the veil, condemn the provocative acts that create the conditions for a confrontation", he said. "I don't think we should legislate on the issue".
A Corsica mayor became the third in France to announce a ban on burqinis on Monday, two days after a massive brawl broke out on the island over the full-body swimsuit.
But Sisco Mayor Ange-Pierre Vivoni was adamant his decision was "nothing to do with racism, it's about protecting people's security".
The French political establishment backs the bans, however, from the Socialist Prime Minister Valls to far-right leader Marine Le Pen, who said on her blog that, "What is at stake is the soul of France".