CAIRO — Egypt, a fecund breeding ground for Arab and Islamic ideologies, is witnessing the birth of yet another: Islamic liberalism.

Nageh Ibrahim, the ideologue of the Islamic Group, an umbrella organization for Egyptian militant student groups that in the 1980s and 1990s took up arms against President Hosni Mubarak, was one of the first to use the term, in an apparent bid to woo secularists into a rapprochement.