The cabinet order came as European envoys headed for Cairo to try to ease tensions between the army-installed government and Islamists.
The order to the interior minister raised the prospect of a dangerous showdown just days after 82 people were killed at a pro-Morsi protest in Cairo.
It came as diplomatic efforts to find a peaceful way out of Egypt's crisis gathered pace, with the EU and Germany sending envoys to urge a peaceful resolution to the standoff.
Adding to the tensions, judicial sources said prosecutors had referred the Muslim Brotherhood's fugitive supreme guide, Mohammed Badie, to trial for allegedly inciting the killing of protesters.
The cabinet's announcement came in a statement that said pro-Morsi protest camps at two Cairo squares were posing a "threat to national security."
However the statement was met with immediate defiance by the Brotherhood supporters, who have been camped out for weeks calling for the reinstatement of Morsi.
"Nothing will change," said Gehad El-Haddad, a Brotherhood spokesman for the coalition protesting Morsi's overthrow, dismissing the order as an "attempt to terrorize Egyptians."
In Rabaa al-Adawiya, the mood was calm after the announcement, with preparations for the Ramadan fast-breaking meal underway and no sign of an immediate increase in the security presence.
Thousands of people have been camped out in a protest tent city at the square.
The interior ministry had already warned that the demonstrations would be dispersed "soon," but without saying when or how.
An interim cabinet minister said Wednesday's statement did not "give room for interpretation."
Confrontations between Morsi loyalists and security forces have turned increasingly deadly, with 82 people killed in clashes with police on Saturday morning.
And at least 51 people were killed in earlier violence between demonstrators and soldiers outside Cairo's Republican Guard headquarters.
NJF/NJF