The elite Counter Terrorism Service (CTS) soldiers had faced fierce resistance from the militants in the area, who launched waves of suicide bombing and sniper attacks.
An airstrike targeted a location thought to contain militants.
The terrorists later retaliated with a car bomb which injured at least one person.
Most residents have chosen to remain in their home despite the fighting, said Alaa Yousef.
"Small clashes are taking place, I think the (Islamic State militants) are on the edges of Tahrir, towards the end. But in general the situation is much better. We will stay home, most people have stayed home, more than 90 percent are in their homes," said Yousef, a local resident.
"The situation was terrible, they were backwards, uneducated, they provided no services. It was a dark period," he added.
But others could be seen carrying their suitcases and white flags as they attempted to flee Mosul.
On Tuesday (November 15) the CTS said they had taken control of the nearby al-Zahraa area after pushing Islamic State fighters out.
The CTS Special Forces spearheading the advance into Mosul are part of a 100,000-strong force of army, security forces, Kurdish peshmerga fighters and mainly Shi'ite "Popular Mobilisation" forces aiming to drive Islamic State from the largest city under their control in Iraq or Syria.
The operation, which entered its fourth week on Monday (November 14), is the most complex in Iraq in over a decade and is complicated by the presence of the more than one million civilians still living under Islamic State (ISIS / Daesh / ISIL) control.
More than 56,000 people have been displaced because of the fighting from villages and towns around the city to government-held areas, according to U.N. estimates.
The figure does not include the tens of thousands of people rounded up in villages around Mosul and forced to accompany Islamic State fighters to cover their retreat towards the city.
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