‘It’s been our misfortune to have the wrong religion,” Hitler complained to his pet architect Albert Speer. “Why did it have to be Christianity, with its meekness and flabbiness?” Islam was a Männerreligion—a “religion of men”—and hygienic too. The “soldiers of Islam” received a warrior’s heaven, “a real earthly paradise” with “houris” and “wine flowing.” This, Hitler argued, was much more suited to the “Germanic temperament” than the “Jewish filth and priestly twaddle” of Christianity.

For decades, historians have seen Hitler’s Beer Hall Putsch of 1923 as emulating Mussolini’s 1922 March on Rome. Not so, says Stefan Ihrig in “Atatürk in the Nazi Imagination.” Hitler also had Turkey in mind—and not just the 1908 march of the Young Turks on Constantinople, which brought down a government. After 1917, the bankrupt, defeated and cosmopolitan Ottoman Empire contracted into a vigorous “Turanic” nation-state. In the early 1920s, the new Turkey was the first “revisionist” power to opt out of the postwar system, retaking lost lands on the Syrian coast and control over the Strait of the Dardanelles. Hitler, Mr. Ihrig writes, saw Turkey as the model of a “prosperous and völkisch modern state.”

Through the 1920s and 1930s, Nazi publications lauded Turkey as a friend and forerunner. In 1922, for example, the Völkischer Beobachter, the Nazi Party’s weekly paper, praised Mustafa Kemal Atatürk, the “Father of the Turks,” as a “real man,” embodying the “heroic spirit” and the Führerprinzip, or führer principle, that demanded absolute obedience. Atatürk’s subordination of Islam to the state anticipated Hitler’s strategy toward Christianity. The Nazis presented Turkey as stronger for having massacred its Armenians and expelling its Greeks. “Who,” Hitler asked in August 1939, “speaks today of the extermination of the Armenians?”

This was not Germany’s first case of Türkenfieber, or Turk fever. Turkey had slid into World War I not by accident but because Germany had greased the tracks: training officers, supplying weapons, and drawing the country away from Britain and France. Hitler wanted to repeat the Kaiser’s experiment in search of a better result. By 1936, Germany supplied half of Turkey’s imports and bought half of Turkey’s exports, notably chromite, vital for steel production. But Atatürk, Mr. Ihrig writes, hedged his bets and dodged a “decisive friendship.” After Atatürk’s death in 1938, his successor, Ismet Inönü, tacked between the powers. In 1939, Turkey signed a treaty of mutual defense with Britain, but in 1941 Turkey agreed to a Treaty of Friendship with Germany, securing Hitler’s southern flank before he invaded Russia. Inönü hinted that Turkey would join the fight if Germany could conquer the Caucasus.

As David Motadel writes in “Islam and Nazi Germany’s War,” Muslims fought on both sides in World War II. But only Nazis and Islamists had a political-spiritual romance. Both groups hated Jews, Bolsheviks and liberal democracy. Both sought what Michel Foucault, praising the Iranian Revolution in 1979, would later call the spiritual-political “transfiguration of the world” by “combat.” The caliph, the Islamist Zaki Ali explained, was the “führer of the believers.” “Made by Jews, led by Jews—therewith Bolshevism is the natural enemy of Islam,” wrote Mahomed Sabry, a Berlin-based propagandist for the Muslim Brotherhood in “Islam, Judaism, Bolshevism,” a book that the Reich’s propaganda ministry recommended to journalists.