Demonstrators demanding 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, rallies were met with violence from security forces and armed groups, leaving more than 420 people dead and nearly 20,000 wounded -- the vast majority demonstrators.

After violence increased last week, prime minister Adel Abdel Mahdi resigned. Talks to find a replacement intensified this week.

Among those attending the negotiations are two key allies of Iraq's main Shiite parties: Iran's Revolutionary Guards commander Major General Qasem Soleimani and Lebanese power-broker Mohammad Kawtharany, a high-ranking political source told AFP.

"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.

The United States said Soleimani's presence showed that its archfoe Iran was again "interfering" in Iraq.

The United Nations envoy to Iraq called on decision-makers to respond urgently to demands for change.

"Political leaders do not have the luxury of time and must rise to the moment," Jeanine Hennis-Plasschaert said on Tuesday.

- Kurds seek to keep 'gains' -

Demonstrators have protested 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.

Protesters 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 premier was in the offing.

But any successor would need the approval of divided Shiite factions, Kurdish authorities and Iraq's key allies, the US and Iran.

The Kurdistan Regional Government supported Abdel Mahdi and is likely worried by his resignation.

The KRG is prioritising keeping a sizeable share of federal government posts and making sure constitutional amendments do not threaten its recent "gains", said analyst Adel Bakawan.

The Kurdish administration said Tuesday it "hoped for the implementation" of a deal agreed in principle days before the premier's resignation, granting it a share of the 2020 federal budget in exchange for exporting its oil through the national seller.

Other parties were also seeking guarantees, a government source told AFP.

"Political blocs want to maintain their positions," the source said, describing discussions as "very difficult".

- Tensions grip shrine cities -

Parties are considering a six-month "transitional" cabinet to oversee electoral reform before an early parliamentary vote, government and political sources told AFP.

A new electoral law is a key protest demand and is now a centrepiece of proposed reforms, with parliamentary blocs expected to discuss it on Tuesday.

Meanwhile, protests continue.

In solidarity with southern provinces, hundreds of students marched in the multi-ethnic northern city of Kirkuk on Tuesday.

In the shrine city of Najaf, 35 protesters were wounded when plainclothes guards fired shotguns and tear gas on crowds near the tomb of Ayatollah Mohammed Baqir al-Hakim, a cleric who founded a major Shiite political party, medics said.

Najaf has been rocked by violence since protesters torched the Iranian consulate there last Wednesday, accusing Tehran of propping up the government.

Tribal dignitaries called on populist cleric Moqtada Sadr to intervene, his office said. He has yet to respond.

In Karbala, riot police fired live rounds and tear gas at protesters, an AFP correspondent reported.

Police dispatched reinforcements to the flashpoint city of Nasiriyah, where deaths have been highest in recent days, and to Basra.

Some 500 extra officers in Nasiriyah and 150 in Basra reinforced prisons holding accused jihadists, to prevent breakouts amid the chaos.

In Baghdad, authorities announced Tuesday they were releasing 16 detained protesters.

The step came a day after Human Rights Watch accused the government of not doing enough to protect activists.