By Isabel Coles and Stephen Kalin

BAGHDAD (Reuters) - Iraq said on Monday it had made arrests as it investigates allegations that Shi'ite militiamen helping the army retake Falluja had executed dozens of Sunni Muslim men fleeing the city held by Islamic State.

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 Shi'ite faction.

Sohaib al-Rawi, governor of Anbar province where Falluja 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 Falluja, just west of Baghdad, alongside the Iraqi army had already raised fears of sectarian killings.

Iraq's Defense Minister Khalid al-Obeidi said four military personnel were arrested after video footage showed them abusing people displaced from Falluja. He pledged on Twitter to prosecute any serviceman involved in such acts.

"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.

Falluja is a historic bastion of the Sunni insurgency against U.S. forces that toppled Saddam Hussein, a Sunni, in 2003, and the Shi'ite-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 the 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

"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 Shi'ite 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 Falluja.

Iraqi authorities routinely separate males aged over 15 from their families when they manage to escape Falluja, to screen them to ensure they do not pose a security risk and check if they may have been involved in war crimes.

U.N. 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 U.S.-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 Falluja on May 23, with air support from the U.S.-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".

(Additional reporting by Ahmed Rasheed and Stephanie Nebehay in Geneva; Writing by Maher Chmaytelli; Editing by Robin Pomeroy)