Iraqi forces backed by jets and helicopters battled jihadists inside west Mosul on Saturday but still faced a tough and potentially protracted battle to retake the Islamic State group's bastion.

Almost a week into a major push on the city's west bank, they were gaining significant ground, taking on IS on several fronts in one of the most intense phases of the four-month-old operation to retake Mosul.

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Elite forces from the interior ministry's Rapid Response units that retook Mosul airport pressed north towards the city centre but their advance was expected to slow as they moved deeper.

"Right now we're heading towards the Mosul governorate building, we're now about one kilometre from the fourth bridge," the city's southernmost bridge across the Tigris River, Lieutenant Colonel Abdulamir al-Mohammadawi told AFP on the front line.

"We're heading towards the centre and also the Turkish consulate, which we're about 500 metres from," he said, as attack helicopters fired rockets at targets in the Jawsaq neighbourhood.

As they pushed deeper from the outer edges of the city into more densely populated areas, resistance appeared to stiffen.

"Daesh is using houses full of residents as human shields," Mohammadawi said, as tanks and troops rained fire on suspected IS snipers.

Moments later, Rapid Response fighters helped two wounded comrades back to the rear for treatment. They moaned in pain and one wore a tourniquet above his knee after being shot in the leg by a sniper.

An Iraqi female reporter, Shifa Gardi, was killed today when a roadside bomb exploded as she was covering the clashes in west Mosul, her channel said.

The 30-year-old journalist for Kurdish network Rudaw became the second reporter to die since the Mosul offensive began four months ago.

In areas now rid of the jihadists, residents told of their lives under IS rule and celebrated their recovered freedom.

"They made us wear short trousers and beards, cigarettes were forbidden. The women had to cover even their eyes, it was forbidden even for their eyes to appear," said 20-year-old Othman Raad outside his home in Jawsaq.

"Now we feel relaxed, our children are safe, we are safe," he said, even as fighting raged blocks away.

Iraqi forces launched a fresh push from the south on February 19, nearly a month after the eastern side of Mosul was declared "fully liberated".

The west bank of Mosul is where Abu Bakr al-Baghdadi made his only public appearance as IS leader in July 2014 and proclaimed a "caliphate" straddling Iraq and Syria.