The UN humanitarian co-ordinator for Iraq, Lise Grande, told the BBC Iraq had made this its priority when it won back the east of the city.
But the western side, with its narrow streets, may prove a bigger challenge.
Leaflets warning residents of an imminent offensive have been dropped.
Mosul is the last major base of IS in Iraq, and the operation to drive the militant group from the city started in October.
Iraqi government soldiers, Ms Grande said, "need to ensure that that humanitarian concept of operations is adhered to, and that all of the parties to the conflict do absolutely everything they can to ensure that civilians survive the battle, and that they live".
"Absolutely nothing is more important going into the campaign to retake western Mosul," she said.
Iraqi forces recaptured the eastern part of the city earlier this year and have now all but surrounded the western part.
The US-led coalition has been carrying out air strikes on IS targets.
Winning the city back has never been just about the military objective of driving IS out of its stronghold, the BBC's Sebastian Usher says.
Minimising civilian casualties and avoiding reprisals will be key to regaining the trust of the city's population in the Iraqi state itself, he adds.

The unconscious man was found on the Old Shoreham Road at the junction with Lancaster Road at 03:50 BST.
It is believed he was hit by a vehicle which failed to stop. He has potentially life-threatening injuries, Sussex Police said.
Anyone with information is asked to call the police quoting Operation Bycroft.

Three of those executed had been convicted of an attack in Tiananmen Square in Beijing last October, in which five people died, Xinhua said.
The others were found guilty of crimes including bomb-making and arson.
The government has accused separatist militants based in Xinjiang of carrying out a string of recent attacks.
Xinjiang is the traditional home of Muslim Uighurs, who speak a distinct language and have different customs to the majority Han population elsewhere in China.
Huseyin Guxur, Yusup Wherniyas and Yusup Ehmet were "deprived of political rights for life" because of their role in the deadly car crash on Tiananmen Square in October 2013, Xinhua said.
"They masterminded the terrorist attack," the news agency added.
In the incident, a car rammed into bystanders on the politically important Beijing square before bursting into flames.
Two tourists died, along with three of the attackers.
Xinhua named some of the other men who were executed along with the Tiananmen attack perpetrators:
Dilxat Raxit, a spokesman for the World Uighur Congress exile group, called the executions "a typical case of the law serving political ends".
Chinese officials often attribute attacks in Xinjiang to Uighur separatists, accusing them of seeking to establish an independent state called East Turkestan.
Beijing has recently blamed them for an attack in May at a market in Urumqi, that left at least 31 people dead.
It also accused them of being behind a mass knife attack in the southern province of Yunnan in March, in which 29 were killed and more than 130 injured.
Uighur leaders deny they are co-ordinating a terrorist campaign.
They say the government's repressive policies in Xinjiang have provoked the unrest.
Who are the Uighurs?

21 November 2016 Last updated at 11:52 GMT
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The safety of hundreds of thousands of civilians trapped in Mosul is a key priority, the UN has warned, as Iraqi troops prepare to attack Islamic State (IS) militants in the west of the city.
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