Other groups though, in particular those closer to Tehran, are refusing.

Why has the matter come to a head now and what is at stake? Here is what we know.

- Why is it happening now? -

The newly installed Iraqi prime minister, Ali al-Zaidi, last month announced plans for a state monopoly on weapons, drawing praise from Washington's special envoy for Iraq and Syria, Tom Barrack.

The diplomat called it a "significant step forward, which represents the nascent foundation for a renewed Iraqi self-governance" and welcomed the "principled decision" of those groups that are choosing to integrate.

Washington has long wanted to curtail Iran's influence in Iraq, but the start of its war with Tehran on February 28 has given it new momentum.

Iran-backed groups in Iraq have launched numerous strikes against US installations in Iraq since the start of the Middle East war at the end of February.

The strikes have been blamed on pro-Iran groups, against whom the US has retaliated, killing dozens of their fighters.

Washington, which has had troops deployed in Iraq since it invaded in 2003 to overthrow Saddam Hussein, has in turn put pressure on Baghdad to rein in the groups by suspending security assistance and cash transfers of Iraqi oil revenues.

Most payments for Iraq's oil are often made into dollar accounts in the United States, with the money used to pay for imports or flown to the country as cash.

The Coordination Framework, the Shia alliance that holds a majority in the Iraqi parliament and includes several members backed by Iran, announced its support for a state monopoly on weapons.

It also called for the breaking of connections between Iraqi political parties and the former paramilitaries of the Popular Mobilisation Forces or Hashed al-Shaabi.

The Hashed paramilitary coalition was created in 2014 to fight the jihadists of the Islamic State group and were later integrated into the Iraqi armed forces. They include several pro-Iran factions that continue to operate autonomously.

- Who is disarming and who is refusing? -

Among the main groups that have announced plans to integrate into the armed forces are the Imam Ali Brigades and Asaib Ahl al-Haq.

The latter group, which the US designates a terrorist organisation, also forms an important parliamentary bloc with 27 seats. Having refocused on politics, it has distanced itself from Iran and has not taken part in the current war.

Beyond the pro-Iran factions, the influential Shia nationalist chief Moqtada al-Sadr has also announced the complete integration of his armed group into the state.

Meanwhile, Kataeb Hezbollah, the al-Nujaba Movement and the Sayyid al-Shuhada Brigades are among those groups closest to Tehran and remain opposed to disarming.

Zaidi's new government remains incomplete, with nine out of 23 cabinet posts still vacant, including the jobs of defence and interior ministers.

Factions opposed to disarmament are refusing to discuss the jobs so long as foreign forces remain deployed in northern Iraq.

Those forces, including US personnel, are there as part of the international coalition against the Islamic State group. Their mission is due to end in September.

- What will it mean for Iraqi-US relations? -

Iraq has long been a proxy battleground for Iran and the United States, with Baghdad trying to walk a fine line between its two key allies but mutual enemies.

An Asaib Ahl al-Haq official told AFP that Washington was concerned about drones and ballistic missiles capable of reaching Israel.

The Iraqi premier has sought to reassure Washington in order to secure US investment, a source in the Coordination Framework told AFP.

The US wants to see concrete results, Tamer Badawi, an Iraq expert at the London-based Royal United Services Institute said, but "Iran will not allow its local allied parties to be disarmed forcibly".

Tehran, he said, wants its allies to "buy as much time as they can".