The warning came a month to the day after troops swept aside two Islamist protest camps in a deadly crackdown slammed by rights groups.
It also came a day after thousands of protesters rallied in Cairo against the military's July 3 overthrow of Islamist president Mohamed Morsi.
The ministry accused the protesters of committing "many crimes" such as blocking traffic and "kidnapping journalists and confiscating their equipment".
"The ministry affirms that it will confront with utmost decisiveness practices such as blocking roads or obstructing traffic or threatening the security of citizens," it warned.
The Islamists have continued to call weekly rallies, insisting that they are committed to peaceful protest.
Today, roughly 200 protesters in Cairo marched near Rabaa al-Adawiya square which was the site of the main protest camp dispersed a month ago.
Hundreds were killed in the operation to clear the camp and another Cairo sit-in, in what Human Rights Watch described as "most serious incident of mass unlawful killings in modern Egyptian history".
Men, women and children chanting "Rabaa, Rabaa!" marched peacefully in the Nasr City district near Rabaa al-Adawiya today.
"We are holding a symbolic march to show that one month after the Rabaa massacre we have not given up our agitation. It will continue," protester Ahmed Shamseldin, a doctor, told AFP.
Morsi supporters have tried to stage regular protests since the crackdown, but in recent weeks their numbers have sharply fallen amid a sustained campaign by security forces targeting Islamists.
Morsi, the country's first democratically elected president, was ousted by the army on July 3 after massive protests demanding his resignation.
On Thursday, interim president Adly Mansour extended for another two months a state of emergency in force since the mid-August bloodshed, citing security concerns.
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