Celebrations in Cairo's Tahrir Square.

Just after sunrise, hundreds of supporters of the Muslim Brotherhood's candidate Mohamed Morsy pour into the square.

Though official counts will not be announced until Thursday, the Brotherhood says its own calculations indicate a Morsy win over rival Ahmed Shafik in run-off presidential elections.

The claim was swiftly challenged by Shafik, the former prime minister.

Meanwhile a decree from the ruling military council Sunday spelled out limited powers for the new head of state and reclaimed lawmaking prerogatives held by the Islamist-led parliament which was dissolved last week.

Some have called the move a "military coup".

(SOUNDBITE)(Arabic) MORSY SUPPORTER, AHMED FARRAG, SAYING:

"The Military Council, last week, made several announcements and took several positions in an attempt to steal the revolution. And the constitutional decree they issued yesterday in order to take power away from the president will simply not happen."

In Gaza City, supporters of Paletinian leaders Hamas also took to the streets to celebrate the Muslim Brotherhood's declaration.

Sarah Sheffer, Reuters