Iraqi forces are reportedly in the midst of a “final assault” to dislodge ISIS from the city of Fallujah:
State forces including members of an elite counter-terrorism unit are moving into Falluja on several fronts, an official statement said on Monday.
The Iraqi air force and international coalition jets are carrying out air strikes in support of ground troops.
IS fighters are reportedly putting up fierce resistance in some areas, especially around the southern side, leading to fierce battles.
The group is thought to have about 1,200 fighters, the majority from the city itself.
The BBC’s Jim Muir in Baghdad says government forces have taken over two townships on the southern fringes of Falluja, but on other fronts they are some way from the edge of the city itself.
The impression is that the army is trying to close a ring of steel around the city, he says.
Militia leaders taking part have said there is likely to be a pause before the assault on the city centre begins so as to allow more civilians to escape.
The New York Times reported on Saturday that the US is “worried” that the operation to retake Fallujah is relying so heavily on Shiʿa militias and their Iranian backers. Iranian advisers are reportedly embedded with front-line Iraqi troops, and celebrity general Qasem Soleimani, the head of Iran’s Quds Force, is reportedly helping to direct operations personally. Fallujah is still home to tens of thousands of Sunni civilians who have been unable to flee in advance of the attack, perhaps because ISIS fighters have been preventing them from leaving. They’re already starving thanks to the blockade around the city, and now they’re in the path of the offensive to liberate it. The concern is that an overtly sectarian Iraqi force will treat those civilians as ISIS sympathizers and punish them accordingly, when in reality most/all of them have been among ISIS’s biggest victims and the objective should be to save them rather than brutalize them further.
“But wait,” the savvy reader is saying right now. “Isn’t the US doing pretty much the same thing in northern Syria, embedding special forces with the mostly-Kurdish SDF in preparation for an assault on mostly-Arab Raqqa?” Funny you should ask, because that’s pretty much true! The Times article even acknowledges this, before explaining that the two situations are completely different because IRAN BAD:
The battle over Falluja has evolved into yet another example of how United States and Iranian interests seemingly converge and clash at the same time in Iraq. Both want to defeat the Islamic State, also known as ISIS or ISIL. But the United States has long believed that Iran’s role, which relies on militias accused of sectarian abuses, can make matters worse by angering Sunnis and making them more sympathetic to the militants.
See, Iran is relying on militias accused of sectarian abuses! Which could anger Sunnis and make them more sympathetic to the militants! Whereas in Syria, the US is relying on militias accused of ethnic abuses! They could also make matters worse by angering Sunnis and making them more sympathetic to the militants, but in a good way! I guess!
The difference, I suppose, is that in Syria the YPG is refusing to play a leading role in an attack on Raqqa precisely because it realizes how problematic that could be to the overall war effort. But as the Times piece also notes, in Iraq those Iranian-supported militias have agreed not to participate in the attack on central Fallujah, leaving that instead to Iraqi Special Forces, which are seen as non-sectarian, and the Iraqi army, which hopefully won’t engage in any sectarian reprisal attacks either. There’s certainly precedent for this; the militias didn’t participate in the liberation of Ramadi, after all, though that didn’t exactly do Ramadi’s citizens any good since their city was mostly destroyed in the fighting. So while it’s reasonable to be concerned that some part of the Fallujah operation will go wrong, this particular concern, at this particular time, seems motivated more by Iran Derangement Syndrome than anything else. The complaint is more about Iran having influence in Iraq generally than about a legitimate specific problem.
The Foreign Exchanges Companion 
Pardon my ignorance, but how long have Iranian-backed militias been operating in Iraq? Is this normal?
Militias allied with Iran have been operating in Iraq since the US invasion. Asa’ib Ahl al-Haqq, Kata’ib Hezbollah, the Badr Organization, and many others were active in the insurgency and have returned to active duty since Mosul.
I was wondering: during the Occupation days when US troops were being targeted by Shia militias, was it ever conclusively proven that the Iranian government was backing these attacks? I remember hearing differing responses from American officials and military figures. A popular hypothesis was that Soleimani was supplying the militias with IEDs and other things, but other US figures said there was no conclusive proof of this.
I’ve never seen anything conclusively proving that Iran was specifically backing attacks against American soldiers. But their broad general support for several of those militias is pretty well-established.