West Mosul is the Islamic State group's last urban bastion in Iraq, and its recapture would mark the effective end of the cross-border "caliphate" its leader Abu Bakr al-Baghdadi announced from a mosque in the city more than two years ago.
Iraqi forces have yet to advance deep into the west, but the fighting combined with privation and harsh IS rule has already pushed a growing number of civilians to flee.
Field teams received "26,000 displaced people from (west) Mosul during the past 10 days," Jassem Mohammed al-Jaff, the minister of displacement and migration, said in a statement.
Sniper fire is a significant danger in the area, said Kathy Bequary, the executive director of NYC Medics, a group providing emergency care from a mobile clinic.
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"We're seeing a lot of serious gunshot wounds from snipers," Bequary told AFP.
"Most of our patients are combatants, but civilians are affected too. Two days ago, we treated a family -- a mother, father, son and daughter -- who were trying to escape Mosul and were targeted by snipers," she said.
The drive to retake the west of Mosul -- the smaller but more densely populated side of a city split by the Tigris River -- began on February 19, after Iraqi troops retook its east side the previous month.
IS is putting up tough resistance in the southwest of the city, a commander in the elite Counter-Terrorism Service told AFP on Wednesday.
The CTS is fighting "for the (Maamun) Flats area, which is considered very important for control of the Baghdad road and the surrounding neighbourhoods," Staff Lieutenant General Abdulghani al-Assadi said.
The damage in the Maamun area is heavy, with homes destroyed, roads cratered and rows of crumpled cars, some of them piled one on top of another.
IS overran large areas north and west of Baghdad in 2014, announcing a "caliphate" incorporating swathes of Iraq and Syria.