CAIRO—Egypt's Muslim Brotherhood said Wednesday it is committed to enshrining Islamic Shariah law as the main source of a new constitution, seeking to mollify ultraconservative Islamists who accuse the group of not advocating strongly enough for Islamic rule.

Islamic influence in Egypt's governance is the most inflammatory issue following last year's ousting of longtime President Hosni Mubarak. Islamists have swept elections since then, and the Brotherhood's Mohammed Morsi is the president—but the Brotherhood faces criticism from even more stringent Islamists as much as from liberals.

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