In militia bases across Iraq, leaders who spent the past four years in military fatigues are wearing clean-cut suits and welcoming guests. Posters of martyrs lost in the fight against Islamic State adorn meeting room walls, but the photos of the living on the streets outside have taken on a new prominence.

Among banners of candidates’ faces lining every main road in the Iraqi capital are the main protagonists of the Popular Mobilisation Forces (PMF), an organisation widely credited with defeating the terror group and which is determined to parlay its battlefield wins into electoral gains in Iraq’s first national election since 2014.

Of all the candidates, party lists and organisations contesting the poll, the PMF, or Hashd al-Shaabi as they are known locally, stand to gain, or lose, most. Its leader, Hadi al-Ameri, and the incumbent prime minister, Haider al-Abadi are viewed as the preferred candidates of Iran and the US respectively. The PMF itself has become a microcosm of the tussle for influence between both powers.

The shape of a postwar PMF has, to many Iraqis, become just as important as the fate of the country itself. Some senior Iraqi officials say the central issue of Saturday’s ballot is whether the organisation – and its estimated 150,000 members, largely Shia Muslim volunteers – is integrated into the structures of the Iraqi state or instead becomes a powerful autonomous institution.

The poll is being held amid renewed tensions between Iran and the US in the wake of Donald Trump’s decision to revoke the nuclear deal initiated and negotiated by Barack Obama. The move has fed anti-US sentiment on the streets of Baghdad and within the PMF as the vote draws near.

The PMF’s Sheikh Qais al-Khazali, left, and Hadi al-Ameri, right. Photograph: Ali Abbas/EPA

Some Iraqi officials say the withdrawal from the deal will probably make Abadi vulnerable and give Iran more options, because it no longer allows him to balance both sides. It could also give Iran more reason to press its will in Baghdad, eschewing an attritional creep for a more robust push, with an autonomous and powerful PMF effectively acting as a Trojan horse.

“It is almost existential,” said a current minister in regards to the shape of the PMF after the election. “They want to set themselves up as a Praetorian guard, just like the Iranian Revolutionary Guards model. They want a parallel state structure. And this would fundamentally change the way Iraq is governed.”

Sheikh Qais al-Khazali, a senior member of the PMF and leader of perhaps its most dominant faction, Asa’ib Ahl al-Haq, whose political bloc is contesting the poll, said fears of a PMF takeover of Iraq were misguided.

In an interview in his Baghdad headquarters, Khazali said the PMF as an organisation remained loyal to Iraq. Khazali, like al-Ameri, and the PMF’s second in command, Abu Mahdi al-Muhandis, receive significant backing from Iran, and have sent fighters to support Iran’s activities in Syria and elsewhere in the region. But he insisted that Baghdad, not Tehran, sets terms.

“There has clearly been a misunderstanding of the role of our neighbouring states in Iraq,” said Khazali. “Some people think that the Shias of Iraq belong to the Iranians and our loyalties lie with them. This is extremely false. The Shias of Iran are not Sumerians [Iraqis]; they have a different culture and society. They have different values. The movement we have here has absolutely nothing to with Qom [a centre of Shia Islamic teaching in Iran, which rivals Najaf in Iraq]. What happens to the Hashd al-Shaabi will be framed by Iraqis, not Iran.”

Throughout the fight against Isis, and in the three years before the group took over five cities and at least one third of Iraq’s territory, Asa’ib Ahl al-Haq had been one of the country’s most powerful non-state actors. The group was responsible for the kidnap of the British IT technician Peter Moore and four of his bodyguards in Baghdad in 2007. He was released two years later, in return for the release from a US-run prison of Khazali, his brother Laith, and a senior member of Lebanon’s Hezbollah. Moore’s four British bodyguards were killed.

The Iraqi prime minister, Haider al-Abadi, speaks at a campaign rally in Baghdad. Photograph: Hadi Mizban/AP

Now, however, Khazali says Asa’ib Ahl al-Haq is no longer on a war footing and wants to take a stake in the country’s political affairs. He says mistakes have been made, by his group and others. “They said the Sunnis were the terrorists and we were the kidnappers. That has to stop. We need to build a state for everyone.

“The revolutionary guards get approval from religious authorities. The Hashd get their approval from the parliament and they cannot mix politics, religion and cultural issues. They do not follow religious guidance. They are independent.

“We love our country and we don’t want to become sectarian again. We have good intentions and we are prepared to cooperate with everyone.”

PMF fighters – young, battle-hardened and impatient for what comes next – are all over Baghdad. Many offer up videos of clashes with Isis that they keep on their phones. All expect this election to provide clarity, in one way or another.

“The government has been lying to us for ages saying they will incorporate us with the army,” said Baqer Jamal, a PMF fighter. “That we will receive the same wages and privileges. But the government is a liar and a thief. We will not get anywhere.”

Wissam al-Saadi, 38, another fighter, said talk of the organisation transforming into an Iranian Revolutionary Guards model was misguided. “We are an organisation that derives legitimacy from the prime minister, we are not an independent body and we don’t want to be either. We didn’t get much say in this election but hopefully in the next one we shall play a bigger role and legitimise ourselves even further in Iraq and with Iraqis.”

What to do with the organisation is also an issue for Iraqis who did not fight and have no direct stake in the group, such as Kadhem al-Amiri, 73. “Iraq is split in two: the ones who support PMF and the ones who don’t,” he said. Amir Mohammed, 18, and a second man, who called himself Akram, seemed to prove his point.

“Had it not been for them we would still be struggling against Isis,” said Mohammed. “We expect and hope they will join forces with the army.”

Akram took a sharply different view. “The PMF is an Iranian project. They are funded by Iran, they take orders from Iran. The Iraqis will be soon wishing for Isis to be back despite their savagery. A dark cloud is coming our way. We are still far from peace.”

Additional reporting by Nadia al-Faour