CAIRO—Leading Egyptian political parties will back a senior figure in the Muslim Brotherhood's Freedom and Justice Party (FJP) for the assembly's speaker, with another Islamist group and a liberal party taking the deputy posts, an FJP official said on Monday. The prime task of the new parliament, the first elected since an uprising swept Hosni Mubarak from power last year, will be to pick a 100-strong assembly to write a new constitution. Liberals fear that sweeping gains by Islamists in elections will put faith-based parties in the driving seat and lead to more religious strictures. Islamists insist they want an...