This is the second phase of the offensive, which began in October.
The US-led coalition has confirmed that Iraqi forces have advanced in three directions and opened up two fronts in the city.
The Iraqi military now has a foothold in the east of the city.
The fresh offensive follows weeks of inactivity as reinforcements were deployed to bolster existing troop numbers.
The assault is not without controversy all five bridges that once spanned the River Tigris have been destroyed cutting off supplies to and escape from the city.
ISIL claim that a coalition strike on a hospital car park has resulted in civilian casualties including women and children.
The coalition has admitted the attack claiming a van launching rocket propelled grenades had been targeted.
Only later did it come to light that the parking facility was part of a hospital compound.