Three protesters have been shot dead during a violent demonstration outside the Iranian Consulate in the Iraqi holy city of Karbala, police officials have said.

Iraq has seen mass protests in the capital and across the mostly Shiite south in recent days that are fuelled by economic grievances and directed at the government and powerful political parties.

The protesters have increasingly directed their anger at Iran, which has close ties to the government, Shiite political factions and paramilitary groups.

Iraq Protests
Iraqi security forces close the Al-Sanak Bridge leading to the Green Zone during ongoing protests in Baghdad (Hadi Mizban/AP)

On Sunday night, dozens of Iraqi protesters set tyres ablaze in Karbala and attacked the Iranian Consulate, scaling the concrete barriers ringing the building as other lobbed firebombs over the walls.

They tried to bring down the Iranian flag and replace it with the Iraqi one but could not reach it. They then placed an Iraqi flag on the wall around the consulate.

Dozens of protesters chanted “the people want the fall of the regime”, one of the main slogans of the 2011 Arab Spring uprisings.

Iraqi security officials said three protesters were shot and killed while 19 were wounded. Seven policemen were also wounded, they said.

Iraq’s Foreign Ministry condemned the attack on the consulate, saying the security of diplomatic missions was a “red line that should not be crossed”.

More than 250 people have been killed since the protests first erupted early last month.

Iraq Protests
Anti-government protesters gather during wekend protests (Khalid Mohammed/AP)

Security forces in Baghdad have fired tear gas, rubber bullets to keep protesters from breaching barricades on two main bridges heading to the heavily-fortified Green Zone, where the government is based.

Later on Monday, protesters clashed with Iraqi security forces on a third major bridge in Baghdad.

They appeared to have crossed the Al-Ahrar Bridge and reached the headquarters of Iraq’s state-run TV on the other side.

The heavy clashes came a day after Prime Minister Adel Abdul-Mahdi called on the protesters to reopen streets and for life to return to normal. His office is just outside the Green Zone.

Police and hospital officials said at least five demonstrators and a member of the security forces were killed, and that another 60 people were wounded.

An Associated Press reporter saw dozens of protesters racing through the streets carrying several wounded people.

Some protesters hurled rocks at security forces, who responded with tear gas and fired a water cannon.

In southern Iraq, protesters have attacked offices linked to Iran-backed political parties and militias, setting fire to some of them.

Over the last two days, protesters have blocked roads around the main protest site in Baghdad’s Tahrir Square to raise pressure on the government.

Political leaders have expressed sympathy for the protesters’ demands while condemning acts of violence on all sides and calling on the protesters to stop disrupting daily life.

Qais al-Khazali, the leader of one of Iraq’s most powerful Iranian-backed Shiite militias, said in an interview aired on Iraqi TV that the US, Israel, some Arab Gulf nations and local officials are working to “incite strife and chaos” in Iraq.

Al-Khazali, who heads Asaib Ahl al-Haq, or League of the Righteous group, singled out the United Arab Emirates.

He also vowed to retaliate for the death of one of his group’s commanders who was killed recently by protesters in southern Iraq.

“The Americans and the Israelis will pay a price,” he said.

Mostly Shiite militias, known as the Popular Mobilization Forces, mobilised in 2014 to battle the so-called Islamic State group but have since grown into a powerful political faction with close ties to Iran.

The militias have blamed Israel for several drone attacks in recent months that targeted their posts in Iraq and neighbouring Syria.