The bodies of two people were covered in sheets when confirmed dead, the correspondent said, adding another protester had been shot in the head and fell to the ground.

The protestors had streamed towards the Guards headquarters on foot from a Muslim Brotherhood rally that attracted tens of thousands at Cairo's Rabaa al-Adawiya mosque.

They accuse the military of conducting a brazen coup on Wednesday against Morsi, Egypt's first democratically elected president, after millions called for his ouster on the June 30 anniversary of his first turbulent year in power.

Shortly before Friday's rallies, around a dozen low-flying military jets screeched across Cairo.

The show of force failed to deter Morsi's supporters, however.

Shots rang out after one Morsi supporter tried to hang a picture of the ousted leader on barbed wire outside the headquarters, said the AFP correspondent.

He was warned twice by members of the Republican Guard not to approach the building before they started shooting.

Gunfire could then be heard from both directions, and security forces also later used tear gas.

Morsi, who has not been seen since Wednesday, had issued a defiant call for supporters to protect his elected "legitimacy", in a recorded speech aired hours after his removal.

The military had said it supported the right to peaceful protest, but warned against violence and acts of civil disobedience such as blocking roads.

Armed forces were also on high alert in the restive Sinai peninsula, bolstering security after Islamist militants killed a soldier in a machinegun and rocket attack.

Morsi supporters argue the president was confronted at every turn with a hostile bureaucracy left over by former strongman Hosni Mubarak, overthrown in the country's 2011 uprising.

Morsi's rule was marked by a spiraling economic crisis, shortages of fuel and often deadly opposition protests.