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The political alliance led by Iraq's former prime minister Nouri al-Maliki is attempting to woo the country's major Kurdish factions into forming a parliamentary bloc big enough to form the next government, according to sources from within Maliki's coalition.

During landmark negotiations, Maliki is making significant concessions to the Kurds, including handing over the disputed region of Kirkuk as well as giving the Peshmerga forces total security control of Iraqi Kurdistan.

Maliki's State of Law alliance, which has already partnered with Fatah, the political arm of the Shia Hashd al-Shaabi militia who came second in the polls, is making a concerted effort to lure the two major Kurdish parties into his bloc that could see him make a surprise return to the premiership, despite stating in February he was not interested in returning to the post and would rather "stay in the shadows".

Maliki, who was in office from 2006-2014, was sidelined after his tenure brought pervasive corruption and his divisive policies were blamed for the collapse of the Iraqi armed forces and the subsequent rise of the Islamic State group.

Maliki's bloc still could however mount a potentially fatal challenge against the coalition announced on Sunday evening by the winning Sairun alliance led by Shia cleric Muqtada al-Sadr, more than three months after the election took place.

Firebrand populist Sadr has united with the Victory alliance led by current Prime Minister Haider al-Abadi, as well as the Hikma bloc led by Shia cleric Ammar al-Hakim and the mostly Sunni Wataniyya bloc led by former prime minister Ayad Allawi.

The preliminary alliance is the largest announced so far, however at a total of 137 seats, they are still 28 seats short of a parliamentary majority and could still be ousted by a bigger bloc.

Sources from within the State of Law coalition confirmed to °®Âþµº on Monday that Maliki's alliance has been in intensive negotiations with the leaders of the Kurdish factions, including those of the two major Kurdish parties, the Kurdistan Democratic Party and the Patriotic Union of Kurdistan, in an attempt to convince them to join his parliamentary bloc.

The sources added Maliki's alliance has promised the Kurds to "resolve the situation" in Kirkuk and the rest of the areas in northern Iraq currently disputed between the autonomous Kurdish regional government and Iraqi authorities. Maliki and his alliance also reportedly promised the Kurds to allow their Peshmerga forces to take full security control of the autonomous region, as a condition of joining his coalition.

The sources also mentioned the negotiations included promises to grant the Kurds control of sovereign ministries and important services, and the allocation of the national budget to Kurdistan would be protected.

The Kurdish leaders are yet to make public the negotiations or announce if they are to join any such coalition, although this is expected in the coming days.

Following the ratification of the election results on Sunday, after a largely inconsequential vote recount, Iraq's parliament now has 15 days to convene in order to elect the next assembly speaker. Following this, they have 90 days to select a new prime minister, which, if the potential Sadr-led bloc remains the largest, is likely to remain as Abadi. If Maliki's bloc succeeds in outnumbering the rest, he could take office.

In addition, the assembly must elect a new president - a largely ceremonial role - within 30 days of the first session. The new president will then invite the largest bloc in the parliament to form a government.

Read more: Can the Sadrist movement transcend sectarianism in Iraq?

The imminent prospect of this has sparked a flurry of activity as the country's many parties and factions begin negotiating across the country's fractious sectarian and ethnic divides in order to form the winning bloc and thus be able to draw up a government.

Even if the Kurds are on board, Maliki and the State of Law will need to convince several more factions to join their bloc in order to outnumber Sadr and his allies, and time is running out.

On Sunday, Abadi made a televised speech calling on President Fuad Masum to initiate the official process of forming a new government.

"I call on His Excellency, the president of the republic, to initiate calling on the Council of Representatives to convene as soon as possible within the constitutionally designated time and to begin procedures of parliamentary presidency and for the president of the republic to assign the representative of the biggest parliamentary bloc to form the next government," he said.