The US-led coalition is attempting to recapture the Old City from the extremists but the ancient quarters are densely populated and there have been concerns over civilian casualties.
The jihadists have been sheltering behind families, mounting attacks from their homes while terrorising them into remaining in a bid to stave off attacks.
One tactic has been to take up positions inside civilian homes from where they shoot at the Iraqi forces but then escape through holes they’ve punched in the exterior walls.
The IS attacks then invite retaliatory firing causing civilian casualties.
General Abdul Wahab al Saadi of the counterterrorism service told Sky News his men did their utmost to avoid civilian deaths or injuries.
He said: “The civilians are really a big problem and their presence there is causing us a big delay because we don’t fire mortars or airstrikes because we are very, very careful about civilian lives.”
We spoke to fleeing civilians who told us repeatedly of IS using them as human shields.
“They really treated us very badly,” one elderly woman told me. “Very early in the morning they told us we had to be ready to go with them and go forward.”
She added: “We got ready and then by the grace of God, we saw the federal police come forward and we ran to them.”
Hundreds of thousands of civilians are believed to be still in the Old City, terrified but unable to leave and caught in the middle of this intensifying war.
Reporters from a Kurdish news agency claim airstrikes killed more than 130 men, women and children as they cowered in their homes in the western district of Mosul al Jadida.
When the Sky News team was in the area, we witnessed several rockets and machine gunfire by attack helicopters into the heavily-populated area of the Old City.
It was impossible to say where the rockets landed but the US-led coalition insists they only target IS fighters and their equipment.
The Iraqi forces face a resilient and determined enemy whose brutality against the population in Mosul has been repeatedly emphasised by survivors.
:: Watch a special programme, The Battle For Mosul, at 12pm and 7pm on Monday on Sky News.