Since the US-led invasion that overthrew former ruler Saddam Hussein in 2003, Iraqi leaders have struggled to find a balance between two powers competing for influence in the country: neighbouring Iran and its arch-foe the United States.

In January, US President Donald Trump threatened to stop supporting Iraq if Maliki returned to the post.

A source close to Maliki -- a two-time former premier with close ties to Iran -- told AFP "I think it is difficult" for Maliki to become Iraq's next premier.

Other political sources confirmed Maliki's chances have waned.

Trump's ultimatum left Iraqi leaders at a loss, particularly within the Coordination Framework, a ruling alliance of Shiite groups with varying degrees of ties to Iran, that had initially nominated Maliki.

The question of the premiership resurfaced after Iraq's parliament elected Nizar Amedi as the country's new president on Saturday, just days after the ceasefire between the US and Iran took effect.

Leaders of the Coordination Framework are holding talks about the premiership, sources close to the framework told AFP.

Some leaders had preferred to delay the process until they could assess the impact of the ceasefire and US-Iran talks on the region, two sources said.

But, with the country under a caretaker government in recent months, including during the Middle East war that also engulfed Iraq, political pressure has grown to move the process forward.

One source close to the framework said the priority is "national unity, avoiding sanctions on Iraq and problems with the US".

Humam Hamoudi, who heads the Islamic Supreme Council of Iraq and is a key figure in the Coordination Framework, urged on Sunday that the selection of a PM candidate be "unanimous" or by an "absolute majority to ensure political stability."

By convention, a Shiite holds the powerful post of prime minister, the parliament speaker is a Sunni, and the largely ceremonial presidency goes to a Kurd.

In February, Maliki told AFP that he would not withdraw his nomination, while also seeking to allay Washington's concerns.

Several names are circulating as possible candidates, including caretaker PM Mohammed Shia al-Sudani, who had previously expressed hopes for a second term.

Iraq's new president has two weeks to appoint a prime minister nominated by the largest Shiite bloc.

But constitutional deadlines are often missed due to persistent political disputes.