A smaller minority then in other European nations it was after Risorgimento and the liberation of Rome that Italy dismantled one of the last Jewish Ghettos and again only later in the 19th century that Jewish people were granted legal equality. By 1910 Luigi Luzzatti, a Venetian Jew, was elected prime minister demonstrating the level of acceptance of Jews within Italian society and their integration into the middle classes. While the early Fascist press had made attacks on the Jewish population in 1928 Mussolini declared 'Fascism has to contend with too many problems to desire to create more. For us Fascists there can be no antagonism to Jews'. At this stage there were several prominent Italian-Jewish fascists; Margherita Sarfatti a propaganda adviser who is rumoured to of been Mussolini’s lover, Angelo Oliviero Olivetti the most prominent of three Jewish speakers at the Congress of Fascist Culture as well as Ettore Ovazza who marched on Rome in 1922 with another 230 Italian Jews and was later murdered alongside his family by the SS as he attempted to flee across the Swiss border.

According to Renzo De Felice in The Jews in Fascist Italy it was only after continued pressure from Nazi Germany a Manifesto of Racist Scientists appeared in July of 1938, which prepared the way theoretically for biological racism. By autumn of the same year the Mussolini instituted anti-Semitic legislation beginning with the Regio Decreto which restricted property rights and positions available within government. This was a concentrated attempt to isolate Jews and strip them of their wealth which was met with some resistance from gentile Italians. In part this can be explained by the relationship between Fascist Italy and Nazi Germany. Hitler and Mussolini had their first meeting in 1934 after the Italian Fascists had been in power for over a decade. Following the meeting Churchhill would quote Mussolini saying to an aide that he 'didn't like the look of him'. Whether there is any actual truth to this is questionable but it captures how Mussolini saw Hitler as a weak and 'unmanly' figure leading a nation of semi-barbarians. Despite this he recognised the need for an alliance with the Nazi state in face of a Bolshevik East and a Liberal-Capitalist West, especially given the fascists increasingly precarious economic position.

By 1943 Mussolini had been driven from power, in the resulting chaos Nazi forces occupied Rome where many working class Jews still occupied the site of the former ghetto. By September the Nazis demanded a ransom of 50 kilograms of gold or they would begin deporting Jews. This was met but only through assistance from non-Jewish Italians. All the same it wasn't enough to prevent round-ups in Rome and across Northern Italy.
As a Nazi puppet state the Fascists of Salo arrested Jews, sending them to Fossoli where they were deported to camps in Germany by the SS. The US Holocaust museum puts the final figure at 8564 deported with the return of 1009 survivors. Mussolini knowingly contributed to the final solution but engaged directly with it only after the collapse of the North-African front.

As a follow-up question: what about other Axis members and allies? Hungary? Vichy France?

Edited to make it clearer I didn't really mean the Allies but other Axis powers and aligned countries. I think the question about allied knowledge of the Holocaust was asked often before.