Avigur was born in Dvinsk (now Daugavpils in Latvia) under the name Saul Meyeroff (later Meirov; Hebrew: מאירוב), but when his son Gur Meyeroff was killed in the 1948 Arab–Israeli War, he changed it to Avigur, meaning "Father of Gur". Along with Reuven Shiloah, Avigur was instrumental in forming SHAI, the intelligence wing of the Haganah, in 1934. Since 1939 he was involved in the Mossad Le'aliyah Bet operations to smuggle Jews into the British Mandate of Palestine and was named its commander.