Between the years 1973 to 1993, he worked as a teacher and vice principal. Simultaneously, from 1978 to 1993, he was a member of Acre's local council and served in the municipality's committees. In 1993 he was elected to Nahal Iron Regional Council, serving as deputy mayor of the council and later as its mayor. He resigned following his election to the Knesset in 1996.
Since his election, he has served as Chairman of the Internal Affairs and Environment Committee (2000–2001) and as Deputy Minister of Internal Affairs (2001–2003). In the latter post he was assigned to head a commission regarding the status of the Falasha.
In a meeting with MK Ayelet Shaked about Women of the Wall, an Israeli human rights group fighting for the right of Jewish women to pray at the Kotel in their fashion, Azulai referred to them as "provocateurs" and claimed that Reform Judaism is “a disaster for the nation of Israel.” Women of the Wall then voiced a protest: "We expect Ayelet Shaked, like her predecessor, to announce unequivocally that as a woman and a justice minister, she will not sign discriminatory regulations, and will not be a part of exclusion of women from the Western Wall or from any other place. The court has already ruled that these regulations are discriminatory and illegal.” Azulai's comments were also condemned by Rabbi Gilad Kariv, executive director of the Reform movement in Israel, who noted, “If Minister Azoulay cannot function as minister for all the citizens of Israel, then he should resign.”