Some 600,000 people remain in the parts of western Mosul held by ISIL, including 400,000 who are "trapped" in the Old City under siege-like conditions, according to the United Nations.
The Iraqi military launched the most recent offensive on western Mosul, the largest remaining ISIL stronghold in Iraq, on February 19, after retaking the city's eastern side.
Many civilians fear fleeing because of ISIL snipers, but some 157,000 have reached a transit centre since the start of the push, the UN's refugee agency said on Thursday.
IN PICTURES: The battle for western Mosul
"They are desperate for food. They are panicked," Bruno Geddo, UNHCR representative in Iraq, speaking from the centre outside Mosul, told a Geneva news briefing
"The worst is yet to come, if I can put it this way. Because 400,000 people trapped in the Old City in that situation of panic and penury may inevitably lead to the cork popping somewhere, sometime, presenting us with a fresh outflow of large-scale proportions,"
ISIL, which stands for Islamic State of Iraq and the Levant, and is also known as ISIS, overran large areas north and west of the capital, Baghdad, in 2014, including Mosul,
But Iraqi forces backed by US-led air strikes and other support have since regained most of the territory they lost.
The operation to retake Mosul was launched on October 17.
The eastern side of the city was recaptured in a three-month offensive that ended in January, but the west, with its densely populated maze of narrow streets, is thought to pose a greater challenge.
Surrounded by a diverse array of forces, the remaining ISIL fighters are digging in for a fight to the end, using car bombs, snipers and grenade-laden drones to slow the troops' advances.
Source: News agencies