Iraqi forces said they had killed the commander of Islamic State of Iraq and the Levant (ISIL) in Mosul's Old City as the battle for the group's last stronghold in the country focused on a strategic bridge crossing the River Tigris.

Federal police said they killed Abu Abdul Rahman al-Ansary, military commander of the Old City, during operations to clear Bab al-Tob district.

With many ISIL leaders having already retreated from Mosul, Ansary's death comes as a blow to the group as it defends shrinking control of Iraq's second-largest city.

READ MORE: Iraq forces hit stiff resistance in Mosul's Old City

ISIL snipers, however, were slowing the advance of special forces units on the Iron Bridge linking western and eastern Mosul, officers said.

Capturing the Iron Bridge would mean Iraqi forces will hold three of the five bridges in Mosul that span the Tigris, all of which have been damaged by ISIL (also known as ISIS) and US-led air strikes.

The southernmost two have already been retaken.

"We are still moving toward the Iron Bridge. We are taking out snipers hiding in the surrounding building," Brigadier-General Mahdi Abbas Abdullah told Reuters news agency.

Near the Mosul Museum, Iraq forces used armoured vehicles and tanks to attack snipers pinning down troops clearing areas around the bridge.

Fleeing civilians

As fighting intensified on Tuesday, civilians streamed out of western neighbourhoods recaptured by the government. Some pushed children and sick elderly relatives in handcarts and wheelbarrows.

Soldiers packed them into trucks on the Mosul-Baghdad highway to be taken to processing areas.

Ashraf Ali, a nurse who escaped with his wife and two children, said mortar rounds were falling as they fled. They took advantage of the army retaking their district to get out.

"Daesh wanted us to move to their areas but we escaped when the army arrived," he said, referring to the Arabic name for ISIL.

As many as 600,000 civilians are caught inside Mosul, which Iraqi forces have effectively sealed off from the remaining territory that ISIL controls in Iraq and Syria.

More than 200,000 Mosul residents have been displaced since the start of the campaign in October.

Iraq's Ministry of Immigration and Displacement said on Tuesday almost 13,000 displaced people from western Mosul had been received seeking assistance and temporary accommodation each day.

Losing Mosul would be a major strike against ISIL.

It is by far the largest city ISIL have held since their leader, Abu Bakr al-Baghdadi, proclaimed himself leader of a caliphate spanning Iraq and Syria in the summer of 2014.