An Egyptian Health Ministry official, Khaled el-Khatib, was quoted in the media as saying that at least 34 people were killed and hundreds injured in firing today outside the building, where Morsi is said to have been put "under guard".
61-year-old President Morsi was toppled by the powerful military on Wednesday and kept under detention along with some senior aides of his Muslim Brotherhood party.
Meanwhile, in a statement the Egyptian army said, "At dawn, an armed terrorist group tried to storm the Republican Guard (building)... attacking army troops and police."
One army officer had been killed and 40 wounded, it said.
The army arrested 200 attackers, who were carrying guns, ammunition, and Molotov cocktails, according to the state-run MENA news agency.
However, the Muslim Brotherhood contradicted army's statement, saying military opened fired on its supporters, killing several pro-Morsi protesters.
Angry over the incident, the group's political wing, the Freedom and Justice Party, called for "an uprising by the great people of Egypt against those trying to steal their revolution with tanks", media reports said.
It urged "the international community and international groups and all the free people of the world to intervene to stop further massacres ... and prevent a new Syria."
At least 36 people were killed and more than 1,000 wounded in the violence during pro-Morsi protests on Friday.
The military has deployed troops in Cairo and other locations.
Supporters and opponents of the ousted president are regularly organising rival demonstrations, with the former demanding Morsi's reinstatement and the latter supporting Morsi's overthrow.
Brotherhood-led National Alliance in Support of Electoral Legitimacy has vowed more protests in support of the deposed president.