Rasha rummages through her kitchen cupboard and holds up a nearly empty bag of rice -- the last of the stock of supplies for her family of five in Iraqs battleground city of Mosul.

"I don't know what will happen when this runs out," she told AFP, as her five-year-old son Yunus fiddled with a toy bazooka his father made him.

"We are relying on God."

A few blocks away from the home in the densely packed Aden neighbourhood, Iraqi special forces are battling Islamic State (IS) jihadists in grinding house-to-house fighting to oust the group from Mosul, the last major population centre it controlled in the country.

But the family are among the thousands of residents of Mosul sitting tight in areas retaken by government troops and praying that the hurricane of violence will soon pass them by.

While aid agencies estimated that some 200,000 residents could flee the city in the first weeks of the fighting, five weeks into the operation only around 70,000 civilians have fled their homes.

"We've already had three mortars hit our roof," said the mother-of-three.

"I am so afraid for my children."

Power lines are cut, gas for heating is running low, and drinking water is nearly gone.

The only supplies the family receives are the occasional bags of bread and packs of bottled water the troops from Iraq's elite Counter-Terrorism Service (CTS) can bring them.

But -- with temperatures at night dropping below zero Celsius -- the thought of making the perilous journey out of Mosul with three young children to one of the sprawling camps for displaced people seems daunting.

"At least here we have a roof over our head," Rasha said.

'Huge concern'

For humanitarian agencies, trying to reach the people inside the recaptured areas of Mosul is becoming increasingly urgent.

The fighting and high risks mean that aid deliveries have been severely restricted.

The United Nations says it has been able to deliver food to some 37,000 people, but they are on the very eastern fringe of the city.

"Security and access is the big challenge," Inger Marie Vennize, a spokeswoman for the World Food Programme in Iraq, told AFP.

"It is a huge concern for us because we know that people need food assistance."

Aid agencies have urged the Iraqi forces to ensure them with access or open up safe corridors.

Vennize insisted agencies were "discussing everything all the time" for aid to reach people who need it in Mosul, but said air drops for now were not on the table.

With fighting raging against a determined enemy who is unwilling to negotiate, there appears precious little room for manoeuvre and the operation looks set to last weeks, if not months longer.

Maan al-Saadi, a commander with the CTS, insisted that the assault was "ahead of schedule".

But he said IS was using unconventional methods that made retaking territory more arduous.

"They are using car bombs, suicide bombers and civilians as human shields -- this makes it difficult for us."

On Wednesday, pro-government militias west of Mosul said they cut off the last remaining routes from Mosul to IS-held territory in Syria.

And that means the jihadists left in he city -- already willing to blow themselves up in their hundreds to slow the Iraqi advance -- are now almost certainly gearing up for a fight to the death.

"They cannot flee. They have two choices -- give up or die," Saadi said.