Baghdad (AFP) - By torching Tehran's consulates and slapping their muddy shoes against photographs of top Iranian officials, Iraqi protesters have shattered a taboo on public criticism of their influential eastern neighbour.

But even as it faces red-hot rage in the streets, Tehran has consolidated its influence within Iraq's political class and among armed actors, analysts tell AFP.

In the latest expression of fury, protesters crowded around the Iranian consulate -- already emptied of diplomats -- in Iraq's shrine city of Najaf late Wednesday.

Shouting "Iran out, Iran out", they set fire to tyres and other items before storming the consulate itself.

"Iran's interference in Iraqi affairs has angered many Iraqis," a young protester in Najaf told AFP.

"The consular fire is a clear message to Iran to reconsider its role in Iraq," he warned.

It was the second Iranian consulate attacked by protesters since the grassroots movement erupted on October 1 in anger at a government deemed corrupt and inefficient.

With unprecedented bluntness, demonstrators in Baghdad and across the restive south have charged Iran with overreaching.

They say Iran interferes too much in Iraqi politics, holds undue sway among its armed actors and has even hamstrung Iraqi industries by flooding markets with its own goods.

Protesters have slapped their shoes against pictures of Qasem Soleimani to insult the commander of the Revolutionary Guard Corps' foreign operations arm and Tehran's pointman on Iraq.

Soleimani, sources told AFP, has played a key role in convincing Iraqi factions to keep backing embattled Prime Minister Adel Abdel Mahdi, further fuelling protester outrage.

- Unprecedented outcry -

"Anti-Iran sentiment isn't new, but how openly it's being expressed is unprecedented," said Fanar Haddad, an expert at Singapore University's Middle East Institute.

"The epicentre of public anger is at the Iraqi political system, but (anger at) Iran is a by-product of that. You cannot disentangle them."

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For decades, Iran has carefully crafted ties to a vast range of Iraqi political and military actors, from Shiite opponents of ex-dictator Saddam Hussein to Kurdish factions in the north and even Sunni tribes in the west.

Tehran also backs many of the factions in Iraq's Hashed al-Shaabi paramilitary force, formed in 2014 to fight the Islamic State group.

On top of that, it sells crucial electricity and natural gas to supplement Iraq's gutted power sector and is the second-largest source of imported goods, from food to cars.

So when demonstrators hit the streets in outrage at a lack of jobs, unreliable electricity and corruption among the ruling class, Iran was on the brain.

"Iran intervenes in the formation of the government and in the economy, and the parties it supports are the ones dominating political life," said demonstrator Hussein.

Young protesters like him had hoped the defeat of IS in 2017 could usher in a phase of relative stability, financial recovery and even some new political parties, said Maria Fantappie, the International Crisis Group's Iraq analyst.

But their hopes were "crushed", Fantappie said, when they saw the political class, Hashed factions and Iran maintain the same ruling system criticised as corrupt.

"There was a simmering anti-Iran feeling and the uprising lifted the cover on the pot that was already boiling," she told AFP, saying the sentiment was "now on the surface".

- Iran 'cements power' -

The protests have uncovered the enormous rift between the public and the political elite, as well as between rival Iranian and Iraqi religious authorities, Fantappie said.

Iraq's highest Shiite religious authority Grand Ayatollah Ali Sistani has backed the protesters and urged outside powers not to intervene.

Many have interpreted his words as a veiled warning to Tehran, including Sistani's Iranian counterpart -- and rival -- Supreme leader Ayatollah Ali Khamenei.

But swelling public criticism of Iran could also trigger more bloodshed, observers fear.

"The burning of the consulate is obviously a blow to Iran, but it can also be used as a pretence for strengthening the security response," Haddad said.

Indeed, a day after the fire, two protesters were shot dead in Najaf.

Another 25 protesters were killed in the southern hotspot of Nasiriyah as security forces cleared streets and bridges.

"While Iran's reputation and credibility eroded in the public scene, the natural reaction was to cement power in security sector and in politics," Fantappie said.