BAGHDAD - Iraqi government forces killed and tortured civilians south of Mosul, rights groups said on Thursday, the first such reports of alleged abuse in a US-backed campaign to retake the city from Islamic State.

Amnesty International said "up to six" people were found dead last month in the Shura and Qayyara sub-districts who security forces suspected of ties to the ultra-hardline militant group which seized a third of Iraqi territory in 2014.

"Men in federal police uniform have carried out multiple unlawful killings, apprehending and then deliberately killing in cold blood residents in villages south of Mosul," said Lynn Maalouf, deputy director for research at Amnesty's Beirut office.

Human Rights Watch (HRW) said at least 37 men suspected of being affiliated with Islamic State had been detained by Iraqi and Kurdish forces from checkpoints, villages, screening centres and camps for displaced people around Mosul and Hawija, further south.

Relatives said they did not know where most of the men were being held and had not been able to contact any of them while in detention, according to the report.

HRW warned that such conduct "significantly increases the risk of other violations", including torture.

An Interior Ministry spokesman denied there had been any violations and said Iraqi forces respect human rights and international law. A spokesman for Iraq 's federal police could not be reached for comment.

A spokesman for the Kurdish regional government denied the HRW report, saying any delays in informing families were limited and due to limited resources.

"Nobody has been kept in unknown facilities. They are kept in identified facilities," said Dindar Zebari.

The Mosul operation, involving a 100,000-strong alliance of troops, security forces , Kurdish peshmerga and Shi'ite Muslim militias and backed by US-led air strikes, has entered its fourth week but has so far gained just a small foothold in the city.

Amnesty's report described several incidents on or around Oct. 21 in which separate groups of men were beaten with cables and rifle butts before being shot to death. In one case, a man's head had been severed from his body, it said.

Amnesty said that, without accountability, the alleged abuses risked being repeated in other towns and villages as the Mosul offensive continues.

Meanwhile, the battle for Iraq 's second city Mosul neared the remains of ancient Nimrud on Thursday, the military said, raising fears for the famed heritage site already ravaged by militant bombs and sledgehammers.

Troops and allied militia were advancing on two villages held by the Islamic State group near the ancient site some 30 kilometres (20 miles) south of Mosul, the Joint Operations Command said.

"Units of the 9th Armoured Division and the Hashed al-Ashaeri (tribal militia) are beginning to advance to liberate the villages of Abbas Rajab and Al-Nomaniyah, toward Nimrud," it said, later announcing that Abbas Rajab had been retaken.

Nimrud was the one of the great centres of the ancient Middle East. Founded in the 13th Century BC, it became the capital of the Assyrian empire, whose rulers built vast palaces and monuments that have drawn archaeologists from around the world for more than 150 years.

Many of its monumental stone sculptures and reliefs were taken away for display in museums around the world but some of the more massive structures remained in place when the militants swept through in mid-2014.

In April last year, IS posted video on the internet of its fighters sledgehammering monuments before planting explosives around the site and blowing it up.

It was part of a campaign of destruction by the militants against heritage sites under their control that also took in ancient Nineveh on the outskirts of Mosul, Hatra in the desert to the south and Palmyra in neighbouring Syria. But that has not stopped the group from trafficking artefacts it purports to revile on the black market to fund its operations.

It is unclear what still remains of Nimrud's ancient ruins as Iraqi forces move closer.

But it is just one of a number of treasured heritage sites that are threatened with further damage by the offensive that the government launched on October 17 to retake Mosul, the militants' last major stronghold in Iraq .

The area where ancient Hatra is located may see fighting between IS and pro-government militias who aim to retake the town of Tal Afar, which commands Mosul's western approaches.

Ancient Nineveh is also in the path of advancing troops.