They asked protestors to defend what they call Egypt's "Islamic identity".
A friend of one of the dead told AFP that police had fired randomly on protestors.
But the interior ministry said police had come under fire, and had arrested a protestor carrying a shotgun.
In a separate development, gunmen in Cairo shot dead an Egyptian brigadier general and wounded two soldiers, the military said.
Several high-ranking security officials have been killed since Mr Morsi was ousted.
Protests elsewhere in Cairo and other regions of Egypt were quickly dispersed by police.
Mr Morsi's Muslim Brotherhood had said it supported the protests but did not say whether it would take part.
His overthrow and detention was followed by a crackdown against his supporters, with hundreds killed and many more arrested.