A German Muslim leader is drawing a parallel between a nationalist party and the Nazis after a prominent party member said that Islam is incompatible with Germany's constitution.

Alternative for Germany, or AfD, has seen its support swell on opposition to the migrant influx to Europe. It also has talked tough about Islam, which deputy leader Beatrix von Storch described in a weekend newspaper interview as "a political ideology that is incompatible with the constitution." She advocated a ban on minarets and muezzins.

Aiman Mazyek, the head of Germany's Central Council of Muslims, retorted Monday that AfD itself "does not conform with the constitution."

He told NDR radio that "for the first time since Hitler's Germany, there is a party that discredits an entire religious community and existentially threatens it."