Minister Mohammed Ibrahim said lawsuits filed by residents near a mosque provide legal cover for the clearance.
But thousands of protesters insist they will stay at Rabaa al-Adawia mosque.
The area was the scene of bloody clashes between the army and protesters on Saturday, with doctors estimating that more than 100 people were killed.
The health ministry puts the death toll lower, at 65.
Mr Morsi's Muslim Brotherhood has blamed the military for the deaths, accusing soldiers of shooting to kill.
The government has denied this, insisting security forces only used tear gas, not live rounds.
The BBC's Quentin Sommerville in Cairo says this appears to be untrue given the severity and number of injuries.
Tear gas, shotgun pellets and bullets were all in evidence during the fighting, he says.
Meanwhile, two leading figures who backed the army's removal of Mr Morsi, on 3 July, have condemned Saturday's killings.
The Grand Imam of Al-Azhar mosque - the highest Sunni Muslim authority in Egypt - has called for an investigation, while the vice-president of the interim government, Mohamed ElBaradei, said that excessive force had been used.
US Secretary of State John Kerry said in a statement that he was deeply concerned about the recent bloodshed.
"In this extremely volatile environment, Egyptian authorities have a moral and legal obligation to respect the right of peaceful assembly and freedom of expression," he said.
Earlier, a spokesman for EU foreign policy chief Catherine Ashton said she "deeply deplores the loss of life" on Saturday and urged all sides to halt the violence.
'Shooting to kill'Saturday's clashes, which began before dawn and carried on for several hours, were the most serious bout of violence since Mr Morsi was ousted.
It appears they began after some of the Morsi supporters tried to extend the barricades around their protest site, and the security forces responded."When I arrived, bullets were whizzing past my ears," he told the BBC.Ahmed Nashar, a Brotherhood spokesman, witnessed what happened.
"Today was just brutal - people were fired at, with live firearms."
Medics at a nearby field hospital told the BBC they believed about 70% of the casualties were caused by live fire - with many of the victims hit in the chest or head by snipers firing from rooftops.
"They were mostly killed by bullet wounds, especially by snipers, especially in the head. We have nearly cut throats, just like animals," said Doctor Hesham Ibrahim.
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A field hospital in Cairo has been treating injured supporters of Mohammed Morsi
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