Speaking to French daily La Croix, Cazeneuve reiterated the government's opposition to legislating on the controversial matter which has sparked fierce debate both at home and abroad about women's rights and France's strictly-guarded secularism.
Around 30 coastal resorts have recently banned women from wearing the full-body swimwear on their beaches, although France's highest administrative court on Friday overturned the measure in one town, in a ruling likely to set a legal precedent which will affect the others.
Rightwing figures are pushing for a nationwide ban to be written into law, led by former president Nicolas Sarkozy who this week launched his bid to regain the presidency in next year's election.
But Cazeneuve ruled out any such move.
"As the prime minister has said, the government refuses to legislate on the matter because any such law would be unconstitutional, ineffective and likely to create antagonism and irreparable tension", he said.
"However, Muslims must continue to engage with us over gender equality, the inviolable nature of the principles of the French Republic, and tolerance in order to live together," he said, noting that in overruling the ban, the court had "stated the law".
Cazeneuve will on Monday have "a day of consultations" with religious figures, civil groups, parliamentarians and others on Islam in France, seeking to get the religion which is the subject of fevered debate throughout the country better "anchored in the values of the Republic".
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'Racists don't plant bombs'
France has been hit by a string of Islamist attacks over the past 18 months, raising questions over security failures and resulting in a spike in Islamophobia.
In the latest instance of intercultural tensions, a restaurant owner in the Paris suburb of Tremblay-en-France is facing an investigation after chasing two veiled Muslim women out of his premises on Saturday.
His actions, caught on video, provoked a furious response and prompted prosecutors to open an inquiry.
The incident, filmed by one of the two women and posted online, shows the other saying; "We don't want to be served by racists".
The restaurateur responds: "Racists like me don't plant bombs and don't kill people."
He added that "terrorists are Muslim and all Muslims are terrorists. I don't want people like you in my place. Now you know it you can get out".
The boss of "Le Cenacle" restaurant later apologised for his actions as calls to boycott his establishment flooded social media sites alongside negative reviews.
A source close to the investigation said that the proprietor had left his home along with his family for security reasons.
Cazeneuve lashed out the opposition for trying to earn political points from the burkini controversy at a time when the country has been rattled by a string of deadly attacks claimed by Islamic State militants.
"Certain opposition leaders are making a lot of noise. They think that in the current context of terror threats, we can abandon the fundamental principles of law as embodied in the Constitution," he said, warning that such a move would be "a serious mistake".
