Two protesters have been killed after supporters of the Muslim Brotherhood clashed with police in Cairo and other cities across Egypt, in a show of defiance despite a state crackdown on the Islamist movement.

Islamists opposed to the army's overthrow of President Mohamed Mursi have been holding daily demonstrations in Cairo and in other cities since the army-backed government declared the Brotherhood a terrorist group last month.

One demonstrator was shot dead by police in the Suez Canal city of Ismailia after a march set off from a mosque after midday prayers, medical sources said.

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In the rural province of Fayoum, southwest of Cairo, a protester died from a bullet wound to the head.

The violence took place less than two weeks before a vote on a new constitution, a milestone in the road map that army-backed authorities say will pave the way for a return to democratic rule by next summer.