Hameiri was born as Avigdor Menachem Feuerstein in 1890, in the village of Odavidhaza (near Munkatsch), Carpathian Ruthenia in Austria Hungary. Growing up with his grandfather instilled in him a love for the Hebrew language. Even though most of mainline Hungarian Jewry was still anti-Zionist, he had already developed an admiration for Zionism when he moved to Budapest.