Upvote:2
Strictly speaking, Hitler modeled his party on Mussolini's principles, and his regime and Mussolini's are often lumped together under the umbrella of fascism. Fascism is a pseudo-religion, a.k.a. an ideology of sorts. The philosophical wing of Hitler's propaganda machine linked fascism to Nietzsche's writings in which Nietzsche submitted that all hopes for the betterment of humanity lay with the arrival of a Superman who would use force to make us peons into a better race. Mercy and sympathy were not supposed to factor in the equation.
The competing propaganda machines (British, American, and Soviet) branded Hitler's party as fascist. Hitler himself had no objections.
The term fascism comes from the Italian fascismo, which in turn is derived from the Latin word fasces (a bundle of rods carried by Roman law enforcement people). The Roman Empire allusion was used by Mussolini, and also by Hitler: the Nazis' "Third Reich" was supposed to be the successor of Constantinople (which would have been the second "reich," the first being Rome itself. (Long before Hitler, Ivan the Terrible of Rus called Moscow "the Third Rome": there's nothing new under the sun).
The answer to your question, then, is this: officially, no; unofficially, yes.
Upvote:10
The answer to your question is: Yes. The Communist Party of Germany (KPD) referred to the Nazis as "Faschisten" long before the Nazis came to power. Their struggle against the regime (once the latter was in place) was called "antifaschistischer Widerstand" (anti-fascist resistance).