But even as Mr. Ameri was fishing for broad support and recognition, his group stands among the most divisive in Iraq, accused of atrocities against Sunnis and known for its close ties to Iran. The new government of Prime Minister Haider al-Abadi, which has promised to rule inclusively, has been under pressure to distance itself from retaliatory attacks against Sunnis by both Shiite and Kurdish militiamen.

At the same time, Mr. Ameri’s boast rings true: His militia has been among the most effective fighting forces against the Islamic State, gaining ground even as the Iraqi Army has faltered in many places despite support from American airstrikes and trainers.

Now, the Badr Organization’s leaders have asserted that their fighters and other allied militias — organized under the banner of “popular mobilization” forces — are ready to advance to neighboring provinces and other Iraqi cities menaced by the Islamic State: a shadow army to Iraq’s official security forces, flush with its own success…

Fears of retaliation by the militias in Diyala grew last month after residents of the Sunni-majority village of Barwanah accused Shiite militiamen of executing 72 people. Mr. Ameri and other Badr officials have denied that their fighters were responsible, even as they have promised to clamp down on abuses.