Iraqis, particularly in Sunni-dominated Anbar, are wary of the militias and the Shiite-led government in Baghdad. Last year, the Islamic State had capitalized on Sunni grievances as it gained strength.

At the same time, the Shiite militias began taking on a role as proxy government fighters as they moved beyond their traditional strongholds in Baghdad and Iraq’s Shiite-dominated south.

Jawad al-Talibawi, a spokesman for the armed wing of Asaib Ahl al-Haq, one of the Iranian-aligned militias, said the group had mobilized 1,500 members of its special forces to enter Anbar.

“Those 1,500 fighters are now awaiting the order to go in,” Talibawi said by telephone.