A US-trained Iraqi army division allegedly executed dozens of men in the final phase of the battle against ISIL fighters in Mosul's Old City, Human Rights Watch has claimed.

The rights group on Thursday urged the US government to suspend all support for the 16th Division of the Iraqi army pending an investigation into what it called war crimes, evidence of which was seen by two international observers whom the group did not name.

The claims could not be independently verified as Iraqi authorities have restricted media access to the Old City since July 10, following Prime Minister Haider al-Abadi's victory declaration over the Islamic State of Iraq and the Levant (ISIL, also known as ISIS).

Spokesmen for the Iraqi government and military could not be reached for comment.

ISIL made its last stand in the Old City after nine months of urban warfare with Iraqi forces, who are backed by a US-led coalition.

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Fighting continued there for several days after victory was declared in mid-July, and videos emerged of Iraqi forces beating unarmed men.

Footage showed one man being pushed off a cliff to his death.

"Given the widespread abuses by Iraqi forces and the government’s abysmal record on accountability, the US should take a hard look at its involvement with Iraqi forces," said Sarah Leah Whitson, Middle East director at Human Rights Watch.

Iraq has promised to investigate previous accusations of abuses and hold perpetrators to account.

The observers cited by HRW said they had seen a group of Iraqi soldiers who identified themselves as members of the 16th Division lead four naked men down an alleyway, after which they heard multiple gunshots.

They were told by other soldiers that the four men were ISIL fighters.

As they were leaving the area, one of the observers saw the bodies of a number of naked men lying in a doorway, one of whom appeared to have been handcuffed and had a rope tied around his legs.

The 16th Division has also been implicated in other executions.

In a separate incident, two soldiers from the same unit showed an observer at least 25 bodies lying on mounds of rubble along the Tigris, and bragged that these were ISIL fighters whom they and their fellow soldiers had executed.

"The US military should find out why a force that it trained and supported is committing ghastly war crimes," Whitson said. "US taxpayer dollars should be helping to curtail abuses, not enable them."