The nationwide state of emergency will be in force from 4:00 pm (7:30 pm IST), the presidency said in a statement read out on state television.
The emergency will be in place for one month. The state of emergency enables the army to take all necessary measures to impose and retrieve security.
The interior ministry issued a statement earlier saying security forces were taking "necessary measures" against the protesters, who want Morsi reinstated, at the Rabaa al-Adawiya mosque in the east of Cairo and the protest in Nahda Square.
Muslim Brotherhood said the actual number of dead was much higher than the 278 reported by the Health Ministry.
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Forty-three members of Egypt's police force were among those killed, Al Jazeera quoted the ministry as saying.
However, Muslim Brotherhood claimed the death toll was as high as 2,200, with about 10,000 injured.
The Interior Ministry said 543 pro-Morsi supporters were arrested nationwide in incidents related to dispersing the Rabaa al-Adawiya sit-in in Nasr City and the Nahda Square sit-in in Giza.
Live footage from Cairo this morning showed smoke engulfing Nahda Square, which was later completely cleared, and there were reports of tear gas and birdshot being used on supporters of Morsi.
Bulldozers were said to have been used to uproot the camps that had been in place after 62-year-old Morsi was ousted by the military on July 3.
In a press conference, the cabinet media adviser thanked the security forces for "exercising self-control and high-level professionalism in dispersing the sit-ins," and held the Muslim Brotherhood responsible for "escalation and violence".
Witnesses said that after firing tear gas into the Rabaa al-Adawiyeh sit-in, pandemonium struck among the thousands of protesters.
Two journalists were also killed while covering the violence today. Mick Deane, a cameraman for the UK-based Sky News channel, and Habiba Abd Elaziz, a reporter for the UAE-based Xpress newspaper, died from gunshot wounds.