The Italo-Turkish war was fought from September 1911 through October 1912 in what is now Libya.
The American Jewish Yearbook roundup of the year's events has a number of entries that shows that the Jews of Palestine solidly supported the Ottoman war effort.
October 15, 1911:
The Anglo-Palestine Bank is the forerunner of the current Bank Leumi.
November 11 and 13:
And here is the really interesting entry, from December 8, 1911:
That's right - the very first Magen David Adom was organized for the purpose of helping mostly Muslim soldiers! (There were some Jewish soldiers in the Ottoman army, and in March the first Jewish officer graduated from the Imperial Military Academy.)
The MDA website says that the first Magen Dovid Adom was set up in 1918 in order to help soldiers of the Jewish Legion and was disbanded after the war. But apparently the first organization to use that name was set up seven years earlier.
While on the subject of the Yearbook, the September 23rd entry is notable:
Also, Arabs killed three Jews and wounded seven on February 3. 1912, showing once again that Arabs attacked Jews way before the fatal events of 1920, 1921 and 1929.
A Report on the Yesha Council at AIPAC
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