Khaled el-Khatib said initial reports indicated that 34 people were killed and 300 others injured in shooting outside the building.
Earlier, Egyptian military officials said gunmen killed at least five supporters of former president Mohammed Morsi and one officer when people tried to storm the building.
A spokesman for Morsi's Muslim Brotherhood and a witness at the scene said military forces opened fire at dawn on protesters staging a sit-in outside the Republican Guard building. The different accounts could not be reconciled.
Satellite broadcaster Al-Jazeera showed footage from a nearby field hospital of at least six bodies laid out on the ground, some with severe wounds. A medic from the area, Hesham Agami, said ambulances were unable to transport more than 200 wounded to hospitals because the military had blocked off the roads.
Al-Shaimaa Younes, who was at the sit-in, said military troops and police forces opened fire on the protesters during early morning prayers.
"They opened fire with live ammunition and lobbed tear gas," she said by telephone. "There was panic and people started running. I saw people fall."
Women and children were among the protesters, she said.
Morsi supporters have been holding rallies and a sit-in outside the Republican Guard building since the military deposed the president during massive protests against him.
The military chief replaced Mr Morsi with an interim leader, until presidential elections are held. But his supporters refuse to recognise the interim leader and insist Mr Morsi be reinstated. Besides the Republican Guard sit-in, they are also holding thousands-strong daily rallies at a nearby mosque.
Mr Morsi's opponents are also holding rival rallies. They say the former president lost his legitimacy by mismanaging the country and not ruling democratically, leading to a mass revolt which called on the army to push him from office.
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