Adel Abdel Mahdi's written statement was greeted with cheers and blaring music across Baghdad's iconic Tahrir Square, where demonstrators have massed since early October against a ruling class deemed corrupt and in hock to foreign powers.

"I will submit to the esteemed parliament a formal letter requesting my resignation from the premiership," Abdel Mahdi wrote, hours after Grand Ayatollah Ali Sistani used his weekly sermon to urge parliament to replace the cabinet.

Abdel Mahdi would be the first prime minister to step down since Iraq adopted a parliamentary system following the US-led ouster of Saddam Hussein in 2003.

"It's our first victory, and we're hoping for many more," shouted one demonstrator in Tahrir as patriotic tunes blasted from motorised rickshaws used to ferry casualties from the square.

Nearby, protesters occupying a gutted 18-storey building that has become a symbol of the uprising danced and pumped their fists in the air.

Many said the premier's resignation did not go far enough, however.

"We won't leave the square until every last one of those corrupt people resigns," said another demonstrator.

"Weed them all out. Every single one."

And despite the joy, security forces dug in behind barricades to keep protesters away from key government buildings, shooting one protester dead, medics said.

- More bloodshed in south -

The grassroots movement is the largest Iraq has seen in decades and also the deadliest, with more than 420 people killed and 15,000 wounded in Baghdad and the Shiite-majority south, according to an AFP tally.

The toll continued to rise Friday, with 15 protesters shot dead in the flashpoint city of Nasiriyah and five killed in clashes in the Shiite shrine city of Najaf.

In Salahaddin, a western Sunni province that has not seen protests, authorities declared three days of mourning for Nasiriyah's victims.

The UN's top official in Iraq, Jeanine Hennis-Plasschaert, said the deaths "cannot be tolerated".

The previous day had been one of the bloodiest yet, with 44 demonstrators killed and nearly 1,000 wounded in Baghdad and across the south.

That came after protesters stormed the Iranian consulate in Najaf, accusing Iraq's neighbour of propping up the Baghdad government.

Tehran demanded that Iraq take decisive action against the protesters, saying it was "disgusted" by developments.

In response, Abdel Mahdi ordered military chiefs to "impose security and restore order", paving the way for a crackdown.

Men in civilian clothes opened fire on demonstrators and tribal fighters deployed in the streets.

As the death toll surged, governors and police chiefs resigned and Abdel Mahdi sacked a senior military commander.

But even after his own declared intent to step down, protesters in the south were not satisfied.

"Our problem isn't the prime minister -- we want all the parties to go!" one man told AFP in Diwaniyah.

- Turning tides -

Since October 1, Baghdad and the south have been rocked by the most widespread street unrest in decades, demanding an overhaul of the ruling elite and reforms to root out corruption, end unemployment and improve infrastructure.

The country is OPEC's second-largest crude producer, but one in five Iraqis lives in poverty and youth unemployment is 25 percent, according to the World Bank.

Abdel Mahdi, 77, came to power last October after a strained alliance between the two largest parliamentary blocs, Saeroon and Fatah.

The protests divided them, with Fatah backing the premier and Saeroon leader and firebrand cleric Moqtada Sadr calling on him to quit.

But they closed ranks around the cabinet following a deal brokered by top Iranian commander Qasem Soleimani.

The tide turned again this week, culminating in Sistani's dramatic intervention.

For weeks, the 89-year-old cleric had called for restraint and urged parties to get "serious" about reform.

But he ramped up his demands on Friday.

"The parliament, from which this current government is drawn, is asked to reconsider its choice in this regard," he said in his weekly sermon.

Within minutes, Saeroon as well as MP and former premier Haider al-Abadi called for a vote of no-confidence.

The Fatah bloc called for "the necessary changes in the interests of Iraq".

Parliament is set to meet on Sunday and if it drops its support for the government, the cabinet would remain in place as caretakers until the president names a new premier.

Iraq's constitution, drafted in 2005, does not include a provision for the resignation of the premier, so submitting a letter to parliament would trigger a no-confidence vote.

The US on Friday called on Iraq's leaders to address "protesters' legitimate concerns", but did not comment directly on the resignation.