The allegations have been denied, but the row highlights the deep sectarian divide that threatens to undermine the fight against IS, even as Government troops make important headway against the extremists.
The latest claims emerged after an unverified mobile phone video was broadcast by a Sunni-run TV station, known for attacking the Shiite-dominated Government in Baghdad.
The video shows an interrogation quickly turning into an outright beating as a prisoner is flogged and repeatedly stomped on the head. It is said to have been shot around Fallujah.
IS are Sunni extremists, Fallujah a Sunni-dominated city, and in the process of flushing-out the extremists, the militias have detained an unknown number of local men.
A member of the local provincial council said some of those detained have been tortured, while a Sunni MP has gone on television demanding to know where other missing men have been taken
Commander prepared for major fight
"For Islamic State, Fallujah is a holy city", the overall commander of this Fallujah operation, Iraqi Lieutenant General Abdelwahab Al Saadi, told the ABC.
"Fallujah fought the Americans and the Iraqi governments and Al Qaeda was well-established there. In short, Fallujah has seen a lot."
Lieutenant General Al Saadi says he still believes locals, alienated by the latest brand of extremists, will support his forces.
"At the very beginning, there was some sympathy from the population towards IS," he said.
"But when they showed their real faces, the Sunnis started rebelling because these groups have no religion and they have no pity for anyone."
It was that trend that helped the Americans prize the city away from Al Qaeda's grip nine years ago.
But since then, many of the Sunni tribal fighters the US paid to help fight extremism have been executed.
Fallujah will be liberated again, but only then will the real test begin, to see whether the sectarian bitterness runs too deep for Iraq to recover.