The Iraqi army says it is getting closer to the main government complex in western Mosul.
A spokesman for Iraq’s military said its Rapid Response forces were within firing range.
The latest push to dislodge ISIL from the city follows Monday’s reported recapture of a key bridge across the Tigris River.
While progress has been steady Iraqi troops have come across stiff resistance from the militants.
That is likely to intensify with most fighting expected to be at close quarters from now on, especially around the old city where ISIL is said to have built a complex network of tunnels.
The advance into the second city comes as the army’s 9th division moves to cut the main road from Mosul to the town of Tal Afar.
The ISIL bastion of Tal Afar has already been cut off from Syria but the goal is to prevent the jihadists from being able to resupply or retreat to the stronghold as Iraqi forces push up from the south.
Meanwhile, civilians continue to stream out of Mosul.
The United Nations has said around 8,000 people have fled the western half of the city, since government forces launched their latest assault just over a week ago.
The UN estimates as many as 750,000 civilians could still be trapped inside Mosul.