The United Nations says about 8,000 people have fled from the western part of Mosul and surrounding villages since Iraqi forces launched the push to take the western half of the city from Islamic State.
The UN humanitarian aid office said on Tuesday those who fled and reached government-controlled areas south of Mosul "are often exhausted and dehydrated."
OCHA says aid agencies and the Iraqi government are expanding displacement sites in the area.
It also says there are "high" trauma casualty rates from western Mosul, with at least 75 civilians treated near the frontlines.
Last week, Iraq launched an offensive to rout IS from Mosul's west, with the support of the US-led coalition. Iraq declared eastern Mosul "fully liberated" in January, after three months of fierce fighting.