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"The factions have presented a conditional ceasefire," Mohammed Mohi, spokesperson for the Iran-backed Kataib Hezbollah group told Reuters.

"It includes all factions of the (anti-US) resistance, including those who have been targeting US forces," he added.

Mohi went on to insist the Iraqi government implement a parliamentary resolution in January to start the US troop’s withdrawal process.

"If America insists on staying," he warned, "and doesn’t respect the parliament’s decision then the factions will use all the weapons at their disposal".

The news comes as tensions between Iran-backed militia and the US-backed government intensified.

At least two people were killed after two separate explosions rocked Baghdad and Anbar, Iraqi security sources said early on Sunday.

"A mentally ill citizen died after entering a booby-trapped house which exploded in Al-Jabal neighbourhood in Rawa district of the Anbar province," Iraq's ministry of defence said in a statement.

Separately, one other person was killed in the capital in a car bombing.

"A sticky bomb attached to the bottom of a car used by a lawyer exploded this evening, as he was passing through Al-Tobij area, west of Baghdad," Baghdad Police Captain Hatem Al-Jabri said.

An investigation has been launched into the Baghdad bombing, Anadolu reported.

Tension between US and the militia

Iraq's Foreign Minister Fuad Hussein has announced that his country has rallied efforts to stop the US from closing its Baghdad embassy, after Donald Trump's administration threatened to withdraw its diplomats if persistent rocket attacks, believed to be from Iraqi militia continued.

Speaking in a televised interview with Al-Iraqiya channel late on Monday, Hussein said "US Secretary of State Mike Pompeo notified Iraqi President Barham Salih of Trump administration's concern over the increased attacks on its mission and the airport, and expressed concern over the security situation".

Hussein pointed out that the "withdrawal of US embassy staff will affect Iraq's relations with other European and Arab missions" and lead to a "lack of confidence in Iraq".

He said that the attacks, blamed on pro-Iran militias, have targeted not only the US embassy but also the Iraqi people as well.

Hussein added that the Iraqi government has taken a "number of security, political and diplomatic measures to stop the attacks on the Green Zone and the Baghdad airport", pledging "tangible positive results in the near future".