Iran-backed majority-Shiite militias known as the Popular Mobilization Units (PMU) have been gaining influence as they have helped the Iraqi army kick the Islamic State (IS) out of Anbar province. Iraq's National Security Council recently blessed their participation in the upcoming battle to retake the IS stronghold of Mosul, while Baghdad announced at the end of July plans to incorporate the militias as an "independent" military formation "affiliated" with the Iraqi armed forces.

The militias have also begun to make diplomatic overtures in a bid to attain international legitimacy. Several militia leaders met with European, Canadian and Australian diplomats in Beirut early last month, Al-Monitor reported at the time, hoping to create a back channel with Washington.

All those efforts now risk running into a congressional buzz saw. Current and pending defense authorization legislation prohibits US military assistance for Iraq if it risks falling into the hands of Iran-backed groups, and lawmakers are keeping a close eye on Baghdad's next move.

"This is an issue," said Sen. Ben Cardin, D-Md., the top Democrat on the Senate Foreign Relations Committee. "We haven't seen the complicity of the Iraqi government to encourage this, but we want to see a stronger effort to discourage it [...]. As a general principle, the Shia militias as currently constituted — and there are some exceptions to this — are not interested in the Iraqi security blueprint and are counterproductive to the security of the areas that we've taken back or want to take back from [IS]."