US-backed Iraqi forces have pushed deeper into the last pocket of Mosul controlled by the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), as the battle for the city approaches an end after seven months of gruelling combat.

ISIL fighters have now been dislodged from all but a handful of districts in the western half of Mosul, including the Old City, where the group is expected to make its last stand, taking advantage of narrow streets and its dense population.

Brigadier General Yahya Rasoul said on Sunday the area controlled by ISIL was no more than nine percent of west Mosul, which is bisected by the River Tigris.

"It's a very small area," he told Reuters. "God willing, this is the final phase."

The Iraqi Counter Terrorism Servicestormed the Ureibi and Rifaie districts at dawn on Sunday, according to a statement from the Joint Operations Command.

At the same time, the army's ninth division and the Interior Ministry's elite Emergency Response Division attacked the ISIL bastion of 17 Tammouz.

"Daesh [ISIL] is drawing its last dying breath," the commander of the ninth division, Lieutenant-General Qasim Nazzal, told state television on Sunday. "Daesh fighters are broken and quickly retreating from fronts."

Vastly outnumbered by the forces arrayed against them, ISIL fighters are fighting back with suicide car bombs and snipers embedded among hundreds of thousands of civilians they are effectively holding hostage.

Hungry civilians eating weeds

There remains concerns about the offensive's toll on the fate of civilians still stuck in ISIL-controlled territories.

Conditions are increasingly desperate; as many are killed, other hungry civilians are resort to eating weeds.

The number of people fleeing Mosul has more than doubled to about 10,000 a day since Friday, according to Iraqi government figures.

Defence analyst and former general Jasim al-Bahadli said the strategy adopted by Iraqi commanders was to splinter the remaining fighters into smaller groups and attack them on multiple fronts to disrupt their command and control.

"By taking back all the districts surrounding the Old City, the militants will have no chance to receive any back-up or reinforcements," he said.

According to the UN, more than 400,000 people have been displaced from western Mosul about two months into the Iraqi army's battle against ISIL.

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The UN Office for the Coordination of Humanitarian Affairs (OCHA) said last week, citing the government, that 434,775 people have fled Mosul - ISIL's last stronghold - since troops launched an operation on February 19.

This brings the number of internally displaced people, since the Mosul operation started in October, to a total of 615,150 Iraqis.

According to OCHA, about 30,000 civilians have returned to their homes in western Mosul since the end of April - meaning that the number of internally displaced people from western Mosul stands at 403,490 people.

Increased ISIL attacks

In recent months, ISIL has stepped up its attacks in different parts of Iraq, apparently in an effort to distract attention from the ongoing US-backed campaign to remove it from Mosul in the country's north.

ISIL seized Mosul, Iraq's second-largest city, in a blitz in mid-2014.

As hundreds of thousands of civilians are still in Mosul, anti-ISIL forces have had to limit their use of aerial attacks and artillery in the city.

Nevertheless, hundreds of civilians have been killed by coalition air raids and shelling, as well as in ISIL's counterattacks.

The US-led coalition bombing ISIL positions in Iraq admitted that it carried out air raids in March at a location in west Mosul, where officials and residents say scores of civilians were killed.

According to Iraq's authorities, ISIL now controls less than seven percent of the country.