In the 12th century religious hermits started inhabiting the caves on Mount Carmel , and in the 13th century they formed a new Catholic monastic order , the Carmelites . Under Muslim rule , the church which they had built on Mount Carmel was turned into a mosque , later becoming a hospital . In the 19th century , it was restored as a Carmelite monastery , the Stella Maris Monastery . The altar of the church as we see it today , stand over a cave associated with Prophet Elijah .