Iraqi politicians and their regional allies gathered in Baghdad on Tuesday to discuss a way out of two months of protests that brought down the government, as violence hit shrine cities. Demonstrators demanding root and branch reform have flooded the capital and the Shiite-majority south since October in the largest grassroots movement the country has witnessed in years. Seen as a threat to the ruling elite, the rallies were met with a heavy-handed response from security forces and armed groups that has left more than 420 people dead and nearly 20,000 wounded -- the vast majority demonstrators. After a fresh uptick of violence last week, prime minister Adel Abdel Mahdi formally resigned and talks to find a replacement have intensified this week in Baghdad. Among those attending the negotiations are two key allies of Iraq's main Shiite parties: Iranian Revolutionary Guards commander Major General Qasem Soleimani and Lebanese power broker Mohammad Kawtharany, a high-ranking political source told AFP on Tuesday. "Soleimani is in Baghdad to push for a particular candidate to succeed Abdel Mahdi," the source said, without providing details. Kawtharany, who is Lebanese militant group Hezbollah's pointman on Iraq, "is also playing a large role in persuading Shiite and Sunni political forces on this," the source added. Political powers in Shiite-majority Iraq have long had close ties with counterparts in Iran and Lebanon further west, both of which have also been rocked by protests in recent weeks. The United States said Soleimani's presence showed its arch-foe Iran was again "interfering" in Iraq, accusing Tehran of having "exploited" the neighbouring country. - Kurds seek to keep 'gains' - Protests in Iraq erupted two months ago over rampant corruption, lack of jobs and poor public services. Despite the oil wealth of OPEC's second-biggest producer, one in five Iraqis lives in poverty and youth unemployment stands at one quarter, the World Bank says. Demonstrators say such problems require more deep-rooted solutions than the resignation of Abdel Mahdi, the first premier to step down since Iraq installed a parliamentary system after Saddam Hussein's overthrow in 2003. The 77-year-old said it would be a "waste of time" to keep a caretaker cabinet in place, in a hint that a political deal to name a new PM was in the offing. But finding a successor appears to have stumped leading political forces, as any candidate would need the approval of divided Shiite factions, Kurdish authorities in the north and Iraq's key allies, the US and Iran. The Kurdish regional government (KRG) was a main backer of Abdel Mahdi and is likely worried by his resignation, observers say, although it has not formally commented. Amid talks in Baghdad, the KRG would prioritise keeping a sizeable share of federal government posts and making sure any constitutional amendments do not threaten its "gains" in recent years, said analyst Adel Bakawan. It would also seek the formalisation of a deal agreed "in principle" just days before the premier's resignation that would grant it a share of the federal budget in exchange for exporting its crude oil through the national seller. Other parties were also seeking guarantees as part of the talks on a new premier, a government source told AFP. "Political blocs want to maintain their positions," the source said, describing discussions as "very difficult." - Tensions grip shrine cities - Government and political sources have told AFP parties are considering a six-month "transitional" cabinet to oversee electoral reform before an early parliamentary vote. A new electoral law has been a key demand of protesters and is now a centrepiece of the government's proposed reforms, with key parliamentary blocs set to discuss it on Tuesday. Meanwhile, protests have continued in the streets of Baghdad and across the south. In Najaf, seat of Iraq's Shiite religious leadership, anti-government demonstrators gathered late into the night around the tomb of a cleric who founded a main Shiite political party, an AFP correspondent reported. Armed guards in civilian clothes were seen firing shotguns and tear gas at protesters, wounding 35, medics said. Najaf has been a flashpoint since protesters torched the Iranian consulate there last Wednesday, accusing Tehran of propping up the government in Baghdad. Around two dozen protesters have died since, and the governor has called on the central government to put an end to the violence. Influential tribal dignitaries have also tried to mediate and on Tuesday they called on populist cleric Moqtada Sadr and his Saraya al-Salam (Peace Brigades) to intervene, according to a statement by Sadr's office. He has yet to respond. In the shrine city of Karbala, riot police fired live rounds and tear gas at protesters late into the night, an AFP correspondent reported.