* Sadr threatens retaliation for killing of followers
* Sadr denies followers fired rockets on Green Zone govt district
* Sadr rival Maliki accused cleric of obstructing Mosul battle
* Demonstrators killed by bullets; suffered choking
* Prime Minister Abadi orders investigation (Adds Sadr denies shelling Green Zone, threat from pro-Iran group)
By Huda Majeed and Ahmed Rasheed
BAGHDAD, Feb 12 (Reuters) - Tension between Iraq's Shi'ite leaders mounted on Sunday as the toll from protests in central Baghdad on Saturday increased to six killed, five demonstrators loyal to the fiery cleric Moqtada al-Sadr and one policeman.
At least 174 other protesters were injured in clashes that pitted police and Sadr's followers who had gathered to demand an overhaul of a commission that supervises elections, ahead of a provincial poll due in September.
The clashes broke out as the protesters attempted to cross the bridge that links Tahrir Square where they had gathered and the heavily fortified Green Zone, which houses government buildings, embassies and international organizations.
In a statement reacting to the killing of his followers on Saturday evening, Sadr said: "Their blood won't have been shed in vain." He promised "peaceful" retaliation.
Several Katyusha rockets hit the Green Zone on Saturday evening but there were no casualties, a military spokesman said.
Sadr's military wing, the Peace Brigades, denied in a statement firing the rockets, reacting to the military spokesman who said they seem to have been fired from Baladiyat, a district where the cleric has many followers.
The growing tensions come at a bad time for Prime Minister Haider al-Abadi who is trying to focus on a critical battle with Islamic State in Mosul, the last major urban stronghold of the Sunni militants in northern Iraq.
Four of the five protesters killed were hit by bullets and the fifth died of unknown causes, according to an updated casualties toll given by an Interior Ministry official. Most of the injured were treated for choking on tear gas, he said.
Sadr says the electoral commission is favourable to his Shi'ite rival, former prime minister Nuri al-Maliki, a politician close to Iran whom he accuses of corruption.
He also blames Maliki for the failure of the Iraqi army to contain the advance of Islamic State in 2014, as he was then prime minister and commander of the armed forces.
The cleric said his supporters wanted to get near the Green Zone to make their voices heard by decision-makers, and had no intention of storming it again.
Abadi ordered an investigation into the violence amid claims by the Interior Ministry that some demonstrators carried firearms and knives. Sadr insists his followers were peaceful.