Their new tactics include circling the Old City using a number of different units which are approaching from different points.
But they are facing strong resistance from a indeterminable number of IS militants who have been bedded down in the ancient quarters for nearly three years and are prepared to die.
The US-led coalition has also faced some tough criticism regarding the rising number of civilian casualties in the battle to drive out the IS terrorists.
We travelled with the Rapid Response Unit (ERD), which is backed up by the Federal Police, as they set off from their base in west Mosul before dawn.
They moved into each suburb extremely carefully, sending in small groups of men on foot to scout the area first.
We were on the edge of the Al-Jadida area where there had already been days of street battles with rubble and bombed buildings all around, but the area was clearly still not entirely secure.
The extremists have a habit of returning to previously cleared areas and mounting attacks from there.
As we entered the area, it was evident there were snipers perched in a number of the higher buildings and they kept shifting their positions.
So as the Forces tried to cross roads on foot, they were shot at.
Several of the tyres on their humvees were targeted and punctured with alarming accuracy.
The job of the foot patrol is to try to determine where the IS snipers are hiding and guide the rest of the forces in that direction so they can be eliminated and the military can advance.
It is far from easy, especially when the military do not know how many civilians may still be in the area or even where they are.
We had been in the area with the Iraqi forces for about five hours and watched them advance slowly along just one street when the first suicide car bomb emerged.
It didn’t drive far. It had probably been hidden for several weeks, maybe longer, in one of the deserted buildings in the centre.
The IS spotters had been watching the Iraqi forces move forward and deliberately waited until they were almost upon them before driving the mobile bomb into the centre of them.
We were with the commander and a small group of his men at the nearest point to the bomb.
It was detonated about 30-40 metres away from us.
But our group was all behind a partially destroyed stone wall which shielded us from the blast. A large fireball followed by dense smoke rose behind the wall.
The men from the Rapid Response Unit, rather than pulling back, instead unleashed a volley of shots towards the buildings in front of them.
Heavy machine gunfire along with rocket propelled grenades and rockets were all deployed.
Two IS drones were spotted in the skies above us. The militants were tracking our movements.
Iraqi snipers attempted to fire them out of the air but the drone just moved higher or beyond reach. Our security adviser Mike Mawhinney spotted a second car bomb heading our way.
“Go left! Go left!” he shouted at us. For one horrible moment, myself and cameraman Garwen McLuckie turned right.
“No, THIS way,” shouted Mr Mawhinney.
We raced after him along with some of the federal policemen. The Rapid Response men were standing their ground and firing ferociously at the car as it ducked between streets trying to find a way through.
An airstrike took it out before it could reach the body of men in the street.
There were clouds of smoke as we scrambled into a building. It was someone’s home.
There was washing still hanging up on the washing line, but IS had also punched a sniper’s hole in the kitchen and created a massive tunnel in the exterior wall as an escape route.
We were waiting in the front hallway of the home as one of the soldiers told us there was intelligence that a third car bomb was on its way. There was a lot of nervous tension in the air.
Everyone knew an attack was headed our way and it would be fierce – but we didn’t know when.
Three of the men were looking out of the front door, trying to peer round the corner as the bomb was detonated.
The blast was so powerful it blew their hats off, shook the building and for one minute, I was worried the walls would collapse.
A short while later, huge streams of people started pouring out from the area where the car bombs had been launched. It seemed they may have been held there by the IS extremists bent on holding on to the area.
Crying women ran past us, most still clad in the all-encompassing black dress and hijab they’ve been forced to wear under IS rules.
Some were clutching babies and toddlers who were either stunned or sobbing themselves.
Some children were running alone. At least one little girl was crying and screaming for her mother. She had lost her in the panic to escape.
The road they were running down was where the Iraqi forces had been shot at repeatedly just a short time earlier by snipers.
A few people kissed the soldiers as they hurried by, losing shoes along the way, so desperate are they to run away from this war.
Gunshots and the sound of bombing were sounding even as they hurried away, leaving everything but what they can carry behind them.
It was a horrifying scene of panic and despair and one which may well be repeated many more times.
And the suicide car bombs will continue to be used to try to stop the Iraqi forces moving forward.
Another has just gone off in west Mosul.
Just another day in the Battle for Mosul.