The fall of Mosul would mark Islamic State's effective defeat in Iraq.
The city is many times bigger than any other that Islamic State has ever captured, and it was from its Grand Mosque in 2014 that the group's leader, Abu Bakr al-Baghdadi, declared a "caliphate" that also spans parts of Syria.
US Defense Secretary Ash Carter said on Tuesday an attack on Raqqa, Islamic State's main stronghold in Syria, would start while the battle of Mosul is still unfolding. It was the first official suggestion that US.-backed forces in both countries could soon mount simultaneous operations to crush the self-proclaimed caliphate once and for all.
The front lines east and north of Mosul have moved much closer to the edges of the city than the southern front and the combat ahead is likely to get more deadly as 1.5 million residents remain in the city.
Worst-case UN forecasts see up to a million people being uprooted. UN aid agencies said the fighting had so far forced about 16,000 people to flee.
"Assessments have recorded a significant number of female-headed households, raising concerns around the detention or capture of men and boys," the office of the UN humanitarian coordinator for Iraq said on Wednesday.
The coordinator, Lise Grande, told Reuters on Tuesday that a mass exodus could happen, maybe within the next few days.
It was also possible that Islamic State fighters could resort to "rudimentary chemical weapons" to hold back the impending assault, she said.
The militants are suspected to have set on a fire a sulfur plant south of Mosul last week, filling the air with toxic gasses that caused breathing problems for hundreds of civilians.
A senior US official said about 50,000 Iraqi ground troops are taking part in the offensive, including a core force of 30,000 from the government's armed forces, 10,000 Kurdish fighters and the remaining 10,000 from police and local volunteers. About 5,000 to 6,000 jihadists are dug in, according to Iraqi military estimates.
Roughly 5,000 US troops are also in Iraq. More than 100 of them are embedded with Iraqi and Kurdish Peshmerga forces advising commanders and helping coalition air power to hit targets. They are not deployed on front lines.The warring sides are not giving casualty figures in their own ranks or among civilians, each claiming to have killed hundreds of enemy fighters.