From an earlier answer of mine plus check out /u/commiespaceinvader 's answer on how Muslims were treated in the Third Reich.

This is a tricky question to answer because there were not all that many truly independent governments in the MENA region during the Second World War. The League of Nation Mandates over former Ottoman domains did create nominally independent countries like Jordan, Syria, and Iraq, but the responsible Anglo-French Mandate powers often had far more say over the running of these countries than their leadership. This would become abundantly clear during the Second World War when the Allied powers did intervene to prevent any foothold of a pro-Axis faction gaining power in the Middle East. A few of these interventions had some merit such as the Anglo-Iraq War of 1941, but others were examples of the Allies really jumping the gun and assuming that anti-imperial rhetoric equated a pro-Axis political orientation. Some MENA leaders went along with events, but others found themselves on the receiving end of a colonial political order. In short, MENA governments were in no real position to aid the Axis war effort in any real fashion, let alone assist in the destruction of European Jewry.

The historiography on the influence of Nazism on various pan-Arab nationalist groups is highly contentious and politicized. There is no shortage of popular commentators post-9/11 that build on linkages between the Arab nationalists in the 1930s and early 1940s and the Third Reich. In some cases, this builds up to a charge that Arab nationalism was a species of fascism and shares many of its precepts of global domination and racism. Conversely, there are commentators that deny the importance of Nazism to the political activism of the thirties and rejects any political connection between fascism and Arab nationalism. Neither approach presents an accurate picture of this period and its complexities.

Again, the situation was complex. While some of the nominal heads of state in the MENA region did aspire to fascist-like national regeneration, this did not translate to alliances with the Axis. Turkey's corporatist model arguably was close to fascism in content, but Turkey hewed to a policy of strict neutrality in the war and sought to exploit both sides for maximum gain without having to become a belligerent. Other MENA governments did not really see much to be gained either from emulation or alliance with Europe's New Order.

In terms of form and some content, several Arab political movements of the 1930s did take some inspiration from the European political scene. Although the NSDAP and Germany were one model to emulate, it was Mussolini, not Hitler, that elicited more interest. With its corporatist model and more intellectually rigorous approach to politics, Italian fascism presented a much more relatable phenomena than Hitler's very German-centric brand of politics. Many Arab nationalist movements within the 1930s looked to Italian fascism as an organizational model, especially its paramilitary formations and leadership cult. The corporatist model had also seemingly worked in Turkey, which added to the attraction of the Italian paradigm in the MENA region. Arab political groups were far from alone in emulating the fascist model. Some Zionist groups and many European nationalist movements such as O'Duffy's Irish Blue Shirts took cues from il Duce in the form of organized paramilitarism and a more militant form of nationalism. Fascism's promise of national regeneration and strength had currency in the context of the demi-colonialism of the Mandate period as it provided both an organizational model for resistance as well as a post-colonial model for government.

One charge often leveled against Arab political movements by the likes of Sam Harris was that they imbibed Nazi antisemitism and this has metastasized in the current invective against Israel. The Mufti of Jerusalem, Haj Amin al-Husseini, was an avowed Nazi sympathizer and active supporter of the Third Reich's actions against the Jews. He did conduct propaganda broadcasts during the war to stir up Palestinians against Zionists and the British occupation. Jeffrey Herf has made much of these broadcasts in his monograph Nazi Propaganda for the Arab World, in which he lays the origin point of Arab antisemitism in these wartime broadcasts. But Herf never really proves that this propaganda found a wide receptive audience within the Arab world. Very few Arabs owned shortwave radios and there is no real evidence one way or the other that they listened to the Third Reich's propaganda. Herf asserts that Sayyid Qutb might have been influenced by these broadcasts, but Qutb's antisemitic essays only appeared in 1951 after the first Arab-Israeli War. Joel Beinin's review of Nazi Propaganda for the Arab World sums up this problematic method rather well and is worth quoting at length:

Herf speaks ominously about “the merging of National Socialist with radical Islamist anti-Semitism and its diffusion to the Middle East” (p. 11). There is no easy way to determine how many Arabs listened to Nazi propaganda broadcasts or their reactions to the message. So, Herf resorts to speculative formulations like, “It is plausible that during World War II, Sayyid Qutb listened to Nazi broadcasts and traveled in the pro-Axis intellectual milieu of the radical Islamists in and around Al Azhar University” (p. 259). We don't know what radio broadcasts Qutb may have listened to. However, because Adnan Musallam's biography of Sayyid Qutb is in his bibliography, Herf should know that it was not until his visit to the United States from 1948 to 1950 that Qutb repudiated Western liberalism and began writing about Islamic themes (Adnan A. Musallam, From Secularism to Jihad: Sayyid Qutb and the Foundations of Radical Islamism [Westport, Conn.: Praeger Publishers, 2005]). Qutb did not join the Muslim Brothers until the early 1950s. His anti-Semitic essay “Maʿrakatuna maʿa al-Yahud” (Our Battle with the Jews) appeared in 1951, after the first Arab–Israeli War. This chronology, although it in no way excuses it, establishes a very different context for Qutb's anti-Semitism. The case for a link between Nazi propaganda and Sayyid Qutb's views about Jews rests on conjecture and innuendo, as does much of what Herf offers when he ventures beyond the terrain of Germany.

Far more persuasive than Herf is the work of Israel Gershoni and James Jankowski who assert that wartime fascist propaganda fell on deaf ears within most of the Arab world. Most Arab public intellectuals saw fascism as a more malignant form of Western colonialism and saw German propaganda as self-serving. Arab political groups may have taken cues from fascism in terms of political self-styling and aesthetics, but this did not translate into sympathy for the fascist cause during the war. Meir Litvak and Esther Webman have backed up this assertion by a deep analysis of Egyptian newspapers that reveals that between 1945-46, they regularly and accurately reported on the Holocaust and expressed a degree of sympathy with the Jewish victims. But the Holocaust generally held only marginal importance within the Arab public sphere and a good many commentators simply noted that it proved that European civilization was not as civilized as colonialist ideologues claimed it to be. The Arab-Israeli wars led to a sea-change in Egyptian papers and then is when Holocaust denial and minimization gained traction within the Arab public sphere.

Even al-Husseini's extremism and involvement with the SS needs a proper contextualization. The Germans never devoted much in the terms of resources or attention to the Arab cause, and most of the conventional bureaucrats in the Italian and German foreign ministries favored other Arab leaders. After the failure of the Iraq revolt in 1941, al-Husseini ended in Europe and worked for the German propaganda machine. But in doing so, he had to compete with other anti-British Arab emigres and navigate the various factions within the German state apparatus. Al-Husseini's anti-Jewish sentiments put him in ideological resonance with the SS, but in light of other emigre competitors like Rashid Ali al-Gaylani, making an alliance with this particular power bloc had a certain political logic behind it. Al-Gaylani's more secular and pan-Arabist politics had found support both in the Italian and German foreign ministries and he was in many ways a more "current" leader against the British, having participated in the Iraqi revolt in 1941. Al-Husseini's main stand against the British had occurred a generation earlier in 1929. Making the most of his connections to Himmler was a way for al-Husseini to gain the paltry resources the Axis devoted to the Arab cause away from an emerging rival.

The above does not to excuse nor does it mitigate al-Husseini's wartime activities. Now al-Husseini very much fits into the mold of being a bad man and a fool, but looking beyond his propaganda broadcasts there was a discernible desperation in his activities for the Third Reich to recognize the cause of Arab independence and place him at the head of it. This was a step that Hitler was unwilling to make and the collapse of the Axis in the Mediterranean made this impossible. al-Husseini helped in the recruitment of Bosnian Muslims in the SS Handschar Division, but he was often quite frustrated that the Germans did not put much weight behind his efforts and the Handschar was not used to fight for Arab independence. The Handschar itself was a failure and suffered severe shortfalls in recruitment numbers and had massive problems with discipline.