Cazeneuve told the Catholic daily La Croix in an interview for Wednesday publication that islamophobic threats or assaults "tripled to some 400 for the year 2015."
He said more than half occurred in the first quarter of the year after jihadists attacked the offices of satirical magazine Charlie Hebdo and a kosher supermarket in January, claiming 17 lives.
Across the year as a whole "we note a drop of five percent in anti-Semitic attacks, which nonetheless remained at a high level with 806 recorded," Cazeneuve said.
The number of anti-Semitic acts in France reached a peak in 2014, when a number of anti-Israel demos led to violence in Paris.
As is often the case, the conflict between Israel and Palestinians in the summer of 2014, spilled over into France which is home to Europe's biggest Muslim and Jewish populations.
Cazeneuve added that attacks on Christian places of worship and cemeteries rose 20 percent to 810.
Overall, 2014 had seen 133 attacks on Muslims and 851 of an anti-Semitic nature based on complaints logged with police.
"I cannot accept such acts - they must be severely punished," Cazeneuve said.
The official tally for 2015 is to be published on Wednesday by Dilcra, the acronym for an inter-ministerial office charged with fighting racism and anti-Semitism.
The massacre by Islamic extremists of 130 people in coordinated Paris attacks in November have also stoked fears of attacks on Muslims and Islamic sites.
Cazeneuve and the French government are desperately trying to keep the lid on rising tensions, which have been stoked by the far right.
The interior minister has repeatedly condemned attacks on Jews, Muslims and Christians.
He said France's Christian roots are undeniable when we look at its history but we "should not create "a reason to exclude those who are not Christians" or "forget their contribution also to the history of our country."
Abdallah Zekri, president of the National Observatory against Islamophobia, said 429 islamophobic attacks or threats had been registered in 2015, the highest since his organization was established in 2011.
(Jewish gravestones knocked over and vandalized in one act of anti-Semitism in France last year. Photo: AFP)
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“Islamophobia must be fought and condemned not only by Muslims but also by the national community as a whole,” said Zekri in a statement. “It is no longer possible to hear and accept that politicians can say that Islam is incompatible with the values of the Republic.”
While the number of anti-Semitic attacks in France may have fallen slightly there has been some shocking incidents in recent weeks, notably the case of a self-proclaimed jihadist attacking a Jewish teacher with a machete in Marseille.
That attack led to a row in the Jewish community over whether men should stop wearing the kippah on the grounds of safety.
"Jews continue to be targeted as specific victims within the national community. It is understandable that some make the choice not to wear signs that can point them out and others leave France for Israel or other countries," said the president of the LICRA (League against Racism and Anti-Semitism), Alain Jakubowicz.