The two-phased polling began amidst tight security. A little more than half of Egypt's electorate of 51 million are eligible to vote in the first round while rest would be able to vote in the next phase on December 22.
The voting, which has so far been peaceful, is taking place in Cairo, Alexandria, Daqahliya, Gharbiya, Sharqiya, Assiut, Sohag, Aswan, North Sinai and South Sinai.
The run-up to the referendum saw deadly clashes between supports of the government and those against it.
The vote on the disputed charter is seen by many experts as a choice between Egypt moving closer toward a religious state led by Morsi's Muslim Brotherhood and the ultraconservative Salafi bloc, or one that retains the secular traditions with an Islamic character.
"I cannot accept such a constitution which aims to trample the rights of the people. This will take Egypt back. The revelution that ousted Mubarak will go waste," said Mohamed Sabry here.
The National Salvation Front of opposition groups organised demonstrations at the presidential palace and in Cairo's iconic Tahrir Square yesterday, after deciding to call on followers to vote "no" in the referendum, rather than a boycott.
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Egypt has been in turmoil for nearly two years after the fall of strongman Hosni Mubarak.
Egypt's Constituent Assembly on November 30 in a marathon session approved the draft constitution imposing Islamic values, a move opposed by Liberals as an attempt to restrict freedom of speech and religion in the country.
The articles passed, stipulated that Islam is the religion of the state, and the principles of Sharia, or Islamic law, are the "main source of legislation".
Mursi then decided to hold a referendum on the controversial draft constitution on December 15, a move that sparked further outrage in the country. MORE