More than two thousand Iraqis in the northern province of Nineveh have been executed by Islamic State militants controlling the area, the defence minister said on Friday in a recorded statement.

Ministry officials could not confirm when or how the deaths had occurred and Reuters was unable to immediately confirm the government's claims.

Access is severely restricted in large parts of Iraq's north and west, which Islamic State militants have controlled since sweeping across the Syrian border in mid-2014 in a bid to establish a modern caliphate.

Witnesses and sources at a morgue in Mosul, the capital of Nineveh, told Reuters that most of the executions reported on Friday had occurred over the past six months.

The majority of the victims, killed for common crimes like theft, had been buried earlier, but the bodies of journalists and former Iraqi police or soldiers were delivered to the morgue earlier on Friday, the sources said. They said IS had circulated lists containing the victims' names.

"(Islamic State) assassinated in cold blood ... 2,070 residents of Nineveh for ... not cooperating with them," Iraqi defence minister Khaled al-Obeidi said in a video posted on the ministry's website.

Interviews with residents in January revealed how Islamic State had created a police state strong enough to weather severe popular discontent in Mosul, the country's second-largest city which fell to the insurgents after Iraqi forces collapsed.

Parliament Speaker Saleem al-Jabouri condemned the reported executions on Facebook as "an historical crime of genocide".

Prime Minister Haider al-Abadi said the killings came in response to Islamic State's losses in Anbar, where pro-government forces launched a campaign last month to roll back the seizure of Ramadi and other areas.

Baghdad and its allies have had to modify expectations of swiftly routing IS there after confronting the reality of a weakened fighting force, sectarian sensitivities in the predominately Sunni province, and political tensions including an Iranian-Western fight for influence. – Reuters