Amnesty made the accusations in a damning 71-page report Tuesday, a day after an offensive led by Iraqi forces was launched to free the city of Mosul from more than two years of ISIS rule.
The report, "Punished for Daesh's Crimes,"
alleges Iraqi security forces and some paramilitary groups under the Popular Mobilization Units (PMU) umbrella carried out routine torture and extrajudicial killings in battles to free cities -- including Falluja this year and Tikrit in 2015 -- from ISIS control. Daesh is the Arabic acronym for ISIS.
The abuse often targeted Sunni-Arab men in apparent "revenge" for attacks by ISIS, the report said. Many of these abuses were committed by Shia groups from the PMU, the report claimed.
"As the battle to retake Mosul gets underway, it is crucial that the Iraqi authorities take steps to ensure these appalling abuses do not happen again," said Philip Luther, Amnesty's research and advocacy director for the Middle East and North Africa.
"The Iraqi authorities must exercise effective command and control over militias, and they must ensure that personnel implicated in past violations do not take part in the Mosul operations."
In response to Amnesty's allegations, Iraq's prime minister, Haider Al Abadi, told a press briefing that he was aware of the report, saying: "I haven't read it. We have established a higher committee to look into these violations, if they exist."
The Kurdistan Regional Government said it has been working with Amnesty International for several months to address these claims -- specifically the destruction of homes, restriction of movement by civilians and the judicial process. A KRG spokesman confirmed that some officials had been punished for the sort of offenses listed by Amnesty. He added that the Iraqi Kurdish President Massoud Barzani and other officials had met with Amnesty representatives and were committed to investigating such allegations.
The report -- based predominantly on interviews with 470 people in July and August -- described several cases of abuse and torture of detainees in counter-ISIS operations. The abuse included electric shocks, beatings with metal bars and pipes, and threats of rape directed against female relatives -- all before the judicial process began, the report said.
In the battle for Falluja, the report said at least 12 men and four boys were executed May 30 after fleeing fighting in al-Sijir. According to survivors quoted in the report, they had handed themselves over to armed men in military and Federal Police uniforms and were told to line up and march forward before being shot dead.
At least 73 other men and boys from the Jumaila tribe in al-Sijir remain unaccounted for.
In another case, PMU militias "abducted, tortured and killed men and boys" from the al-Mehemda tribe from Saqlawiya in June this year, and at least 643 men remain missing, the report said, citing findings by a government investigative committee.
"I was driven to the 'yellow house' at night and put in a room of about 4m x 5m with tens of others. There was blood on the walls. Torture started immediately," Amnesty quoted a survivor as saying.
"They hit us with anything they could lay their hands on, metal rods, shovels, pipes, cables. They walked on top of us with their boots. They insulted us, and said that this was payback ... (for the 2014 Camp Speicher massacre). I saw two people die before my eyes," the survivor continued.
A spokesman for the PMU -- known in Arabic as the Hashd Al-Shaabi -- denied the allegations in the Amnesty report.
"The report is based on information the group had gathered from some politicians with agendas in order to give bad reputation to the Hashd Al-Shaabi who played key roll on liberating towns and city from ISIS," said spokesman Hassan al-Sari. He criticized Amnesty for releasing the report as Iraqi security forces and paramilitary forces are fighting to liberate Mosul, calling it " wrong timing."
ISIS hanged as many as 1,700 men in the Camp Speicher massacre, at what was formerly a US military base near Tikrit.