Iraqi authorities "are following up on the violations and a number of arrests have been made," government spokesman Saad al-Hadithi said after a regional governor said 49 Sunni men had been executed after surrendering to a Shiite faction.
Sohaib al-Rawi, governor of Anbar province where Fallujah is located, said on Sunday that 643 men had gone missing between June 3 and June 5, and "all the surviving detainees were subjected to severe and collective torture by various means."
The participation of militias in the battle of Fallujah, just west of Baghdad, alongside the Iraqi army had already raised fears of sectarian killings.
"Harassment of IDPs (internally displaced persons) is a betrayal of the sacrifices of our brave forces' liberation operations to expel Daesh (Islamic State) from Iraq," he said.
Fallujah is a historic bastion of the Sunni insurgency against US forces that toppled Saddam Hussein, a Sunni, in 2003, and the Shiite-led governments that followed.
In the north of the country, troops fought with Islamic State militants in the village of Haj Ali for the second day in a row, an Iraqi officer taking part said.
Haj Ali is near Qayyara, a town under Islamic State control which has an airfield that Baghdad's forces seek to use as a staging ground for a future offensive on Mosul, about 60 km (40 miles) north.
"Strict orders were issued to protect the civilians," government spokesman Hadithi said, adding that these instructions were also given to the Hashid Shaabi, or Popular Mobilisation Forces, the coalition of mostly Shiite militias backed by Iran which are involved in the fighting.
The United Nations said last week it knew of "extremely distressing, credible reports" of men and boys being abused by armed groups working with security forces after fleeing Fallujah.
Iraqi authorities routinely separate males aged over 15 from their families when they manage to escape Fallujah, to screen them to ensure they do not pose a security risk and check if they may have been involved in war crimes.
UN human rights chief Zeid Ra'ad al-Hussein said screening was legitimate but should not be done by paramilitary groups.
"The country must avoid further divisions or violence along sectarian lines, lest it implode completely," he said on Monday.
A spokesman for the US-led coalition fighting Islamic State said the Baghdad government was aware of the abuses.
"We know that the prime minister has come out and said that he believes that these abuses have happened and that he... has demanded accountability of any perpetrators," Colonel Chris Garver said. "We think that is the right course of action."
The Iraqi army launched the offensive on Fallujah on May 23, with air support from the US-led coalition. The United Nations has said up to 90,000 people are trapped in the city with little food or water.
Repeated phone calls to three spokesmen of the Popular Mobilisation Forces were not answered. Last week, one of them, Kareem Nuri, said past accusations of human rights violations were "politically motivated and baseless."