Over 10,000 ultraconservative Muslims demonstrated Friday in downtown Cairo to demand that Egypt’s new constitution be based on the rulings of Islamic law, or Shariah, 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 longtime autocrat Hosni Mubarak and ushered in the rise of formerly repressed Islamists to power. But Islamists themselves are not in agreement over the interpretation of Shariah and its place in the document.

Demonstrators in Tahrir Square demanded that the Muslim Brotherhood, the powerful Islamist group from which the country’s new President Mohammed Morsi hails, override liberal and secular objections and include language that could see religious scholars influencing what can become law.

‘‘Shariah is our constitution,’’ and ‘‘The people demand the application of God’s law,’’ they chanted.

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