The Muslim Brotherhood says its members were fired on while they were holding a sit-in at a Presidential Guard barrack.
But the army said a “terrorist group” had tried to storm the barracks.
Mohamed Morsi, an Islamist and Egypt’s first freely elected president, was ousted by the army last week after mass protests.
Dozens of people have been killed since the unrest began last weekend.
Mohamed Morsi is believed to be held at the Presidential Guard Club, in the eastern Nasr City district of the capital.
His supporters – many of them members of the Muslim Brotherhood movement he comes from – have been staging a sit-in there demanding his reinstatement.
After Monday morning’s violence, the hardline Salafist Nour party – which had supported Mohamed Morsi’s removal – said it was withdrawing from talks to choose an interim prime minister, describing the shooting incident as a “massacre”.
There were conflicting reports from Cairo over how the violence had unravelled in the early hours of Monday morning.
The Muslim Brotherhood said the army raided its sit-in at about 04:00 as protesters were performing dawn prayers.
The Freedom and Justice Party, the Brotherhood’s political wing – which took nearly half the seats in last year’s historic election – called on Egyptian’s to stage an “uprising” in response to the incident, against “those trying to steal their revolution with tanks”.
It also urged “the international community and international groups and all the free people of the world to intervene to stop further massacres” and to stop Egypt becoming “a new Syria”.
But in a statement read on state media, the army blamed the shooting on “an armed terrorist group” that had tried to storm the barracks.
It said an army officer was among those killed and that a number of others were wounded, some critically.
The statement said some 200 people had been arrested and were found to have weapons, ammunition and petrol bombs.
TV channels broadcast images of dead and injured people being taken to a makeshift hospital in the Rabaa al-Adawiya mosque, where Brotherhood supporters have been based.
Nour party spokesman Nadder Bakkar said Nour had “decided to withdraw immediately from all negotiations in response to the massacre”.
Though the Islamist party had backed the army-led “roadmap” to new elections, it had been wary of the Muslim Brotherhood becoming isolated.
It had blocked the appointment of two potential prime ministers it thought would not include the movement in the political process.
Mohamed Morsi was replaced on Thursday by Adly Mansour – the head of the Supreme Constitutional Court. He has pledged to hold elections soon, but has as yet given no date for them.
The army has insisted it does not want to remain in power.
On Sunday, tens of thousands of both supporters and opponents of Mohamed Morsi rallied in many Egyptian cities.
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