The latest reports from different right groups showed Iraqi government forces killed and tortured civilians south of Mosul, Reuters reported on Thursday.
It is the first such reports from rights groups of alleged abuse in a U.S.-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 jihadist 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 centers 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 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.
Amnesty's report described several incidents on or around October 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.