“The cabinet has decided to take all measures necessary to confront these risks and put an end to them,” an official said in a televised statement.
The statement termed the continued rallies “a national security threat”.
Three top Muslim Brotherhood leaders have also been referred to court on charges of inciting violence.
The movement’s supporters have staged sit-ins for several weeks since President Morsi was removed on 3 July.
They have defied previous threats of removal from their sit-in protests, despite deadly clashes with security forces.
The main protest sit-in is at a square near the Rabaa al-Adawiya mosque in the capital’s north-east, where deadly clashes erupted on Saturday killing 70 people, and in Nahda Square near the main campus of Cairo University.
“The continuation of the dangerous situation in Rabaa al-Adawiya and Nahda squares, and consequent terrorism and road blockages are no longer acceptable given the threat to national security,” Information Minister Dorreya Sharaf el-Din said, speaking in a televised statement.
Mr El-Din said the police had been tasked to end the demonstrations “within the law and the constitution”.
The interim government had earlier warned that any violation of the law would be dealt with “firmly”.
Last week, the army called on its supporters to take to the streets to give military chief Gen Fattah al-Sisi a mandate to deal with violence and “potential terrorism”.
Also on Wednesday, Egyptian prosecutors referred Muslim Brotherhood leader Mohammed Badie, his deputy Khairat al-Shater and senior leader Rashad Bayoum to trial over allegations of inciting the killing of protesters last month.
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