The militias have plagued U.S.-linked diplomatic and military targets for months, firing rockets at embassies and bases and targeting Iraqis who drive logistics convoys serving the U.S.-led coalition.

The Trump administration has responded by threatening to shutter the U.S. Embassy in Baghdad, a move that Iraqi officials say will accelerate Iran’s ascent in the tug of war that the two countries have fought over Iraq since the 2003 U.S.-led invasion.

Mohammed Mohie, a spokesman for the Iran-backed Kataib Hezbollah group, said Sunday that attacks would halt while the militias waited for the U.S.-led coalition to detail its timeline for full withdrawal. “But this truce is conditional, and the condition is that we will accept their retreat,” he said. He did not provide a timeline for the process.

Mohie said he spoke on behalf of the Iraqi Resistance Coordination Commission, a new body that announced itself with a similar statement Saturday. Neither Mohie’s comments nor the statement appeared to have come in consultation with the U.S.-backed force to which it referred. The U.S.-backed force did not respond to requests for comment on the matter.

It was unclear how many groups the new body represented.

Iraq’s parliament urged the expulsion of U.S. troops in January, after President Trump ordered the killing of Iranian Maj. Gen. Qasem Soleimani in Baghdad. Soleimani had been a talismanic figure for Iraq’s militias. Also killed in that strike was Iraqi militia leader Abu Mahdi al-Muhandis.

The strike sent tensions between Washington and Tehran soaring. Iraqis braced for the confrontation.

Since then, the U.S.-led coalition has departed from smaller bases across Iraq and promised to reduce its troop presence from 5,200 to 3,000. Although the coalition officially attributes that move to the Iraqi military’s increased capacity to take on what remains of the Islamic State militant group, senior officials have acknowledged that it came in response to concerns about the heightened risk of attacks by Iran-backed militias.

In the event that the U.S.-led coalition does not provide clarity on its timeline for withdrawal, Mohie said, the militia factions would use “all weapons available to them.”

Kataib Hezbollah is one of a handful of powerful Iran-backed groups that have served as part of Iraq’s conventional security forces since helping Iraqi and coalition forces defeat the Islamic State in the country.

But in recent months, apparent splinter groups have taken responsibility for rocket and roadside bomb attacks. Western officials in Baghdad say these are probably front groups for elements within the larger Iran-backed groups, allowing the latter to avoid retaliatory U.S. attacks.

It was unclear whether the weekend’s announcements had altered that playbook.

Iraq’s military reported Sunday that an Iraqi convoy carrying logistics equipment for the coalition was targeted with an improvised explosive device, this time on the highway between Samawah and Diwaniyah in the south.