* Iraqis on the streets for day two of renewed protest wave
* At least 10 people killed on Saturday, 52 on Friday
* Protests aimed at political elite accused of corruption
* Shi'ite heartland rising up against Iran-backed militias (Adds details from Baghdad; political statements)
BAGHDAD, Oct 26 (Reuters) - At least 10 Iraqis were killed and dozens wounded on Saturday, police and hospital sources said, as demonstrators and security forces clashed in a second day of protests against Prime Minister Adel Abdul Mahdi's government.
The unrest followed violence on Friday in which at least 52 people were killed around the country as protesters vented frustration at political elites they say have failed to improve their lives after years of conflict and economic hardship.
In Baghdad, security forces lobbed tear gas to try to disperse demonstrators in Tahrir Square. Four were killed after being struck directly in the head by tear gas canisters, police and hospital sources said. Two people were in critical condition from similar injuries.
Abdul Mahdi chaired a meeting of his top security commanders on Saturday night, as security forces attempted to clear the square ahead of Sunday's start to the work week.
By nightfall, members of the security forces issued warnings on loudspeakers, lobbed a volley of tear gas at the crowd and chased protesters into narrow side streets.
Four protesters were killed and 17 people were wounded amid chaos in the southern city of Nasiriya, where demonstrators came out in their thousands despite the heavy presence of security forces.
The deaths occurred when a group of protesters broke off from thousands gathered in central Nasiriya to storm the house of a local security official, police said. Guards opened fire after the protesters torched the building, police said.
Two more people died during protests in Hilla.
Earlier in October, 157 people were killed and more than 6,000 wounded in other clashes between protesters and security forces.
The unrest has broken nearly two years of relative stability in Iraq, which from 2003 to 2017 went through a foreign occupation, civil war and an Islamic State (IS) insurgency.
It posed the biggest challenge to Abdul Mahdi since he took office just a year ago. Despite promising reforms and ordering a broad cabinet reshuffle, he has so far struggled to address the protesters' discontent.
Adding further pressure to his premiership, the parliamentary bloc linked to Shi'ite cleric Moqtada al-Sadr announced it was going into opposition on Saturday.
As sirens wailed and tuk-tuks ferried bloodied protesters to hospitals, others expressed outrage at a political establishment so willing to resort to violence.
"The (political) parties today after 16 years have only robbed and plundered," said 33-year-old demonstrator Silwan Ali.
"Our protests are peaceful, we only have flags and water bottles, but they keep firing bombs at us, firing tear gas at us; what have we done to deserve this? What have we done? The young men who died, what did they do?" he said.
As violence continued to engulf the country on Saturday, political leaders spoke out in support of security forces' actions, while militia leaders signaled their support for security forces' tough stance against protesters, and urged the premier not to back down.
The United Nations' Iraq Envoy Jeanine Hennis-Plasschaert said the actions of "armed entities, eroding government's credibility and ability to act, cannot be tolerated."
Iraq's military and Ministry of Interior said in morning statements that they planned to respond more firmly to protests on Saturday.
Whereas on Friday tear gas was used only to repel those who approached the capital's fortified Green Zone housing government buildings and foreign embassies, security forces were using it on everyone in Tahrir Square on Saturday, at one point throwing canisters into the crowds roughly every 15 minutes.
In Baghdad protesters distributed masks and homemade remedies to protect themselves from the tear gas. Others handed out food and water.
Most of those killed on Friday were protesters in cities in the south. Eight others were killed in Baghdad, most after being struck by tear gas canisters.
On Friday, demonstrators focused their anger on politicians and Iranian-backed Shi'ite militia groups.
Members of the powerful Asaib Ahl al-Haq (AAH) militia turned their guns on protesters in both Nasiriya and Amara, leaving scores dead. AAH also clashed with another powerful militia, one loyal to populist cleric Moqtada al-Sadr.
Despite a curfew and federal anti-riot forces dispatched from Baghdad, thousands gathered across cities in the south.
Protesters continued to torch the offices of all major political parties, militia groups, and local government buildings. In Nasiriya, they set fire to the governor's house.
Security forces began making arrests in Nasiriya at nightfall, with officials worried that the violence could spiral further.
"This is not a protest, this is a revolution," said one protester who declined to give his name.
'STEALING FROM US'
Parliament was set to meet on Saturday in an emergency session to discuss the protesters' demands, but with many politicians keeping a low profile since the protests began it failed to reach a quorum and the session was canceled.
"The government has been stealing from us for 15 years. Saddam went and 1,000 Saddams have been hiding in the Green Zone," a protester who declined to be named said on Saturday, referring to the former Iraqi dictator.
The Interior Ministry praised what it called the restraint shown by security forces on Friday.
"The security forces secured the protection of demonstrations and protesters responsibly and with high restraint, by refraining from using firearms or excessive force against demonstrators," it said in a statement on Saturday.
But with fears of spiraling violence in the south, security forces said they would not shy away from using force to quell protests.
In Basra, police said protesters who attacked security forces, public, and private property would be prosecuted under Iraq's strict counter-terrorism law. (Reporting by Ahmed Aboulenein; Additional reporting by Ahmed Rasheed in Baghdad, Aref Mohammed in Basra, and a Reuters correspondent in Nasiriya; Writing by Raya Jalabi; Editing by Frances Kerry, Hugh Lawson and Chizu Nomiyama)