Prime Minister Adel Abdel Mahdi, as commander in chief of the armed forces, dispatched military chiefs to several restive provinces to "restore order" there, the military said in a statement.
Iraq's capital and its south have been torn by the worst street unrest since the 2003 US-led invasion that toppled Saddam Hussein, as a youth-dominated protest movement has vented their fury at their government and its backers in neighbouring Iran.
Iran vows to punish 'mercenaries' behind street violence
Late Wednesday protesters burnt down the Iranian consulate in the city of Najaf, yelling "Victory to Iraq!" and "Iran out!", in an attack condemned by Tehran which voiced its "disgust".
Iraq's death toll in the street clashes since early October has risen above 360 with over 15,000 wounded according to an AFP tally, as authorities are not releasing updated or precise figures.
Protesters burning tyres and throwing rocks and petrol bombs have clashed with security forces unleashing tear gas, rubber-coated bullets and live rounds.
The latest clashes erupted on Thursday in the protest hotspot of Nasiriyah, where security forces cleared protesters off two main bridges they had been occupying for days.
At least 13 protesters were shot dead and 100 wounded with several in critical condition, medical and security sources said.
Hours later, local authorities declared a curfew and military reinforcements were seen deployed around the edges of the city, searching all cars and people seeking to enter, AFP's correspondent said.
The order echoed a similar one enforced overnight in the holy city of Najaf in response to protesters storming the Iranian consulate there.
Demonstrators across the country have blamed Iran, Iraq's powerful eastern neighbour, for propping up the very government they seek to topple.
On Thursday morning, streets in Najaf were largely deserted due to the curfew, with public servants told to stay home.
Iran meanwhile demanded Iraq take decisive action against the protesters, with foreign ministry spokesperson Abbas Mousavi condemning the attack.
"Iran has officially communicated its disgust to the Iraq ambassador in Tehran," he said in comments carried by Iran's state news agency IRNA.
In a dramatic scene late Wednesday, protesters lit tyres and other random items around the consulate in Najaf, sending tall flames and thick clouds of smoke into the sky, an AFP correspondent reported.
The protesters broke into the building itself, which had been apparently evacuated by its Iranian staff.
"Victory to Iraq!" and "Iran out!" they chanted.
Iran's consulate in Iraq's other holy city of Karbala was targeted earlier this month, and security forces defending the site shot four demonstrators dead at the time.
Iran and Iraq have close but complicated ties.
The two countries fought a devastating 1980-1988 war, but Iran now has significant sway among Iraqi political and military leaders.
US says will sanction Iran 'abuses' against protesters
Top Iranian commander Qasem Soleimani, Tehran's point man on Iraq, has held several meetings in Baghdad and Najaf to convince political factions to close rank around the government of Abdel Mahdi.
Those meetings previously paved the way for a brief crackdown in Baghdad and the south.
The security response on Thursday appeared to be coordinated across provinces, with the military command saying "an emergency unit has been set up under the supervision of the governors" to "impose security and restore order".
That included a unit in Dhi Qar province, where Nasiriyah is located.
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