“No one can stop us from going there,” Amiri said Saturday at a commandeered farmhouse about a mile west of Fallujah.

Such a move into Fallujah could cause serious problems. In early 2014, the Islamic State easily took control of the city by exploiting the anger of its residents against the Shiite-dominated government in Baghdad.

And Sunni leaders from the area, in Iraq’s western Anbar province, have expressed extreme discomfort with the presence of the militias. Human rights groups have accused Shiite militiamen of brutal treatment of Sunnis suspected of ties to the Islamic State.

Iraqi Prime Minister Haidar al-Abadi has vowed to address Sunni grievances, which include allegations of neglect and discrimination by authorities. And the Iraqi military has ordered most of the militias — formally called the popular mobilization units — to keep out of Fallujah. The units are mostly Shiite groups, some of them backed by Iran, but they also include smaller outfits of Sunnis, Christians and other religions.