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Iraq's security forces need another three months to eliminate the Islamic State group from the country after launching their offensive against IS in October, Prime Minister Haider al-Abadi said on Tuesday.

"The available data indicate that Iraq requires three months to eliminate Daesh," Abadi told a televised news conference, referring to the militant group by an Arabic acronym.

Previously, he had vowed that the IS-occupied city of Mosul would be retaken "before the end of the year", a goal that is no longer possible.

What began as a rapid push into Mosul, which the extremists have occupied since June 2014, has turned into a hellish block-by-block war, with IS inflicting high casualty rates on advancing Iraqi forces.

Since the offensive began on 17 October, elite Iraqi forces have reconquered several parts of eastern Mosul and are moving closer to the Tigris, the river that divides the city, but IS still occupies the city's west.

The Iraqi forces now control 44 percent of Nineveh province, of which Mosul is the capital, spokesperson of the Iraqi joint operations command said on Saturday.

Yahia Rasoul also said that the Iraqi forces now control 40 districts in eastern Mosul.

High-ranking officials believe that the battle against IS could drag on, and the extremist group continues to carry out attacks in areas from which it had been dislodged by the government offensive.

A top US commander predicted on Sunday that it would take at least two years to remove IS from Mosul and its Syria stronghold of Raqqa.

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Speaking to The Daily Beast, Stephen Townsend said that despite Iraqi commanders telling local media that the Mosul assault was going ahead without break, the reality is that they have paused over the last week to resupply.

"People need to rest. They need to assess how things are going because they are not going as fast as we thought," the US commander said, adding that the US had forewarned their Iraqi partners of this.

The Mosul operation slowed down over the past week reportedly over bad weather conditions as well as the fear for civilian lives in targeted areas.

Some 100,000 people have fled Mosul since the Iraqi operation against IS began, and aid organisations have said it could result in the displacement of more than a million people.

The government has encouraged civilians in Mosul - where a million or more people may still live - to stay in their homes if possible.

IS claims responsibility for regular attacks elsewhere in Iraq including in Fallujah, the Sunni-majority city east of Baghdad that was retaken in June after being out of government control for two and a half years.

The militant group overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes have since regained much of the territory originally lost to IS.

Agencies contributed to this report.