Iraqi government forces battling ISIL for Mosul took control of a main bridge over the River Tigris on Wednesday and advanced towards the mosque where the group's leader declared a caliphate in 2014.

The seizure of the Iron Bridge, linking eastern Mosul with the ISIL-held Old City on the west side, means that the government holds three of the five bridges over the Tigris - and bolsters Prime Minister Haidar al-Abadi's assertion that the battle is reaching its final stages.

The gains were made in heavy fighting in which troops fought street by street against an enemy using suicide car bombs, mortar and sniper fire and grenade-dropping drones to defend what was once their main stronghold.

"Our troops are making a steady advance ... and we are now less than 800 metres from the mosque," a federal police spokesman told Reuters news agency.

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The military gains made against Islamic State of Iraq and the Levant have come at a human cost.

Nearly 100,000 Iraqis have fled western Mosul in the past three weeks as government forces backed by Shia militias advanced on territory held by ISIL, the International Organization for Migration (IOM) said Wednesday.

The Iraqi Ministry of Displacement and Migration said that as many as 600,000 civilians remained trapped in neighbourhoods of west Mosul controlled by the armed group.

Iraqi forces and their allies have been making steady progress in the city, forcing ISIL (also known as ISIS) out of a series of neighbourhoods and retaking important sites such as the airport, Mosul museum, train station and provincial government headquarters.

But the battle for west Mosul - smaller and more densely populated than the eastern side, which Iraqi forces recaptured earlier this year - has forced a flood of people to flee their homes.

In recent days, residents have been streaming out of western neighbourhoods recaptured by the government, desperate and hungry and traumatised by living under ISIL's harsh rule.

According to the IOM, between February 25 and March 15, more than 97,000 people were displaced, an increase of about 17,000 from the figure it released on Tuesday.

IOM said that the new figures, provided by the Iraqi government, showed that more than 116,000 people from the city's west had gone through a screening site south of Mosul.

"Some families are still stuck," Hajj Ahmed, a 55-year-old who had recently fled Mosul, told AFP news agency.

"They [ISIL] have been besieging people for seven days," he said, before praising Iraq's elite soldiers for saving them.

READ MORE: 'Exhausted, terrified', 4,000 flee Mosul daily

Federal police officers and a special forces unit advanced on the Nuri mosque, where in July 2014, ISIL's leader Abu Bakr al-Baghdadi proclaimed himself head of the Islamic State caliphate.

ISIL fighters have booby-trapped houses, and government forces have been forced to fight among civilians, ruling out the extensive use of air and artillery support.

ISIL seized Mosul in mid-2014 when the group swept through areas north and west of Baghdad, taking control of swaths of territory and declaring a cross-border "caliphate" in Iraq and neighbouring Syria.

Backed by US-led air strikes and other international military support, Iraqi forces have since retaken much of the territory they lost.

Losing Mosul would be a major blow to ISIL, but the group is expected to pose a continuing threat, reverting to guerrilla-style tactics.