In the statement, the Guardian Council told demonstrators to "end the sabotage and rioting activities" and described the protests as a "conspiracy" against Iran.
Across Tehran, hundreds of arrests have already been carried out.
Most significantly, police detained for a short time Faezeh Rafsanjani, the daughter of former President Akbar Hashemi Rafsanjani, who is Mousavi's chief political backer. She had joined protesters last week, urging them on. The BBC's John Leyne was expelled from the country.
The widening crackdown is a direct response to the deadly clashes that engulfed Tehran overnight Saturday, killing 19, according to state radio.
We spoke with one protester inside Iran who would not allow us to name her out of fear for her safety. She said the protests were for "changing the regime. That's what we're aiming for." Even as authorities continue to crack down hard on protests and the people involved in them, she said, "we're doing our best and if we get enough support it might happen."
The Associated Press contributed to this report.