CAIRO — Over 10,000 ultraconservative Muslims demonstrated on Friday in downtown Cairo to demand that Egypt’s new constitution be based on the rulings of Islamic law, or Sharia, in the latest tussle over the role of religion in the country’s future.

The writing of the constitution has been fraught with controversy since last year’s political uprising that toppled autocrat Hosni Mubarak and ushered formerly repressed Islamists into power. But Islamists themselves are not in agreement over the place of Sharia in the document.