The Islamist rallies have often descended into bloody clashes with security forces, leaving hundreds dead since Morsi's ouster in July.
The government's message has a strong resonance among a public weary of constant protests and unrest.
Rights groups and activists say the law, issued Monday by the interim president, will stifle Islamists and non-Islamists alike.
They say it is harsher than restrictions on protests during the rule of autocrat Hosni Mubarak, who was ousted in 2011 in an uprising calling for greater democratic freedoms.
Announcing the breakup of the protests, a police spokesman said defiance of the law would not be tolerated.
“This behavior is a challenge to the state and its prestige. The protesters want to embarrass the state. But the state is capable,” Maj. Gen. Abdel-Fattah Othman told private CBC TV. “Any gathering without a permit will be dealt with according to the law.”
In Tuesday's first protest, around 100 largely secular activists rallied downtown to commemorate an activist—Gaber Salah, known by the nickname “Gika”—killed by police a year ago.
Police quickly deployed, and an officer told the gathering they had no permit, said activist Rasha Azab, who was among the protesters.
He gave two warnings before the police fired water cannons, sending the protesters running into side streets, she said.
“They don't want anyone in the streets any more. Not us, not the Islamists,” said Azab.
Hours later, a similar group sprung up outside parliament, protesting moves by the panel amending the constitution to preserve a Morsi-era article that allows military trials of civilians. “Down with military rule,” they chanted.
