"What happened today of storming the government's facilities and tampering public property, cannot be accepted," Abadi said. "The law must take its course with every transgressor."
On Friday Iraqi security forces opened fire on protesters who stormed into the Green Zone and entered the cabinet building, drawing calls for revolt from a powerful Shiite Muslim cleric Moqtada al-Sadr.
Dozens of demonstrators were injured by tear gas and live fire, witnesses said. Some security personnel were stabbed, according to a military statement, AP reported.
Authorities could not immediately verify reports that several civilians had been killed.
The thousands of protesters included supporters of cleric Moqtada al-Sadr and people from other groups upset with the government's failure to approve anti-corruption reforms and provide security.
The government briefly imposed a curfew on Baghdad and authorities later said order had returned after what they called rioting at the Green Zone, which houses parliament, government buildings and many foreign embassies.
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