* PM's move is latest twist in crisis
* His departure could be blow to Iranian influence
* Sistani calls on MPs to reassess support for gov't
* Parliament due to meet on Sunday to discuss crisis
* More than 400 killed in unrest (Adds protester death, Baghdad rocket blast)
By John Davison
BAGHDAD, Nov 29 (Reuters) - Iraqi Prime Minister Adel Abdul Mahdi announced his resignation on Friday after the country's senior Shi'ite Muslim cleric urged lawmakers to reconsider their support for a government rocked by weeks of deadly anti-establishment unrest.
Violence raged on in southern Iraq, however, killing at least 21 people, and one protester was killed in central Baghdad as demonstrations continued including a thousands-strong sit-in at Tahrir Square in the Iraqi capital.
Young, unemployed and unarmed protesters have led calls for an overhaul of a political system they say is endemically corrupt and serves foreign powers, especially Baghdad's ally Tehran.
The departure of Abdul Mahdi could be a blow for Iranian influence after Iran's militia allies and its own commanders intervened last month to keep the premier in place despite mass anti-government unrest.
The biggest unrest for years in a country struggling to recover from decades of conflict and sanctions pits protesters from Shi'ite heartlands in Baghdad and the south against a corrupt Shi'ite-dominated ruling elite seen as pawns of Iran.
Iraq's current political class is drawn mainly from powerful Shi'ite politicians, clerics and paramilitary leaders including many who lived in exile before a U.S.-led invasion overthrew Sunni dictator Saddam Hussein in 2003 - including Abdul Mahdi.
"In response to this (the cleric's) call, and in order to facilitate it as quickly as possible, I will present to parliament a demand (to accept) my resignation from the leadership of the current government," a statement signed by Abdul Mahdi said.
The statement did not say when he would resign. Parliament is to convene an emergency session on Sunday to discuss the crisis.
Grand Ayatollah Ali al-Sistani earlier urged parliament to considering withdrawing its support for Abdul Mahdi's government to stem spiralling violence.
Protesters celebrated the imminent departure of Abdul Mahdi, but said they would not stop their demonstrations until the whole of the political class was removed. Violence continued in southern Iraq.
"Abdul Mahdi's resignation is just the beginning. We'll stay in the streets until the entire government has gone, and all the rest of the corrupt politicians," said Mustafa Hafidh, a protester at Baghdad's Tahrir Square.
"It's not enough," said Ali al-Sayeda, another demonstrator. "We need them all out, root and branch. We can't let up the pressure."
A victory for Iraq's national soccer team against the United Arab Emirates gave protesters at Tahrir Square more cause for celebration and they set off fireworks, enjoying a brief respite from the unrest.
Later, security forces shot dead a demonstrator at nearby Ahrar Bridge, police sources said.
Security forces meanwhile shot dead at least 21 people in the southern city of Nassiriya after protesters tried to storm a local police headquarters, hospital sources said. In Najaf, unidentified armed men shot live rounds at demonstrators sending dozens scattering.
Iraqi forces have killed hundreds of mostly young, unarmed demonstrators people since mass anti-government protests broke out on Oct. 1. More than a dozen members of the security forces have also died in clashes. At least 436 people have died in less than two months, according to a Reuters tally from medical and police sources.
The burning of Iran's consulate in the holy city of Najaf on Wednesday escalated violence and drew a brutal response from security forces who shot dead more than 60 people nationwide on Thursday.
Sistani, who only weighs in on politics in times of crisis and wields huge influence over public opinion, warned against an explosion of civil strife and tyranny.
He urged government forces to stop killing protesters and the protesters themselves to reject all violence, in apparent reference to the burning of the consulate in Najaf.
The government "appears to have been unable to deal with the events of the past two months ... parliament, from which the current government emerged, must reconsider its choices and do what's in the interest of Iraq," a representative of Sistani said in a televised sermon.
Some protesters took to the streets in Iraq's northern, Sunni-majority provinces in solidarity with their Shi'ite compatriots in the south, spurred by Abdul Mahdi's resignation and emboldened by the soccer win, Reuters witnesses said.
Sunni areas decimated by the fight to defeat Islamic State have mostly been quiet, partly because of fears that IS militants could exploit unrest to grow an ongoing insurgency.
A rocket hit Baghdad's fortified Green Zone which houses government buildings and embassies late on Friday but caused no casualties, the military said.
Iraq's "enemies and their apparatuses are trying to sow chaos and infighting to return the country to the age of dictatorship ... everyone must work together to thwart that opportunity," Sistani said, without elaborating. (Reporting by John Davison, Baghdad newsroom; additional reporting by Reuters TV; Editing by William Maclean, Angus MacSwan and Daniel Wallis)
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