Iraqi and Kurdish forces say they have secured about 20 villages on the outskirts of Mosul in the first 24 hours of their offensive.
A spokesman for the joint operations command, Brigadier General Yahya Rasool, says troops have not seen any residents fleeing so far.
"Up to now, we have not recorded any displacement cases, and the troops are still advancing. Some of the areas and villages are empty except for members of Islamic State."
The United Nations Refugee Agency says it expects a mass exodus of people from the city and is braced for the first big wave within five or six days.
The organisation Australia for UNHCR has launched an emergency appeal to help the agency provide shelter and protection to civilians.
National director Naomi Steer says the organisation hopes to raise $4 million in Australia to contribute towards the initial response.
"There is a huge gap, unfortunately, between what we have and what is needed currently in funding. UNHCR estimates it has only got about 38 per cent of funding required to provide support to many hundreds of thousands fleeing fighting in Mosul."
The World Food Program has been prepositioning food aid in warehouses near the city.
Spokeswoman Bettina Luescher says it has enough rations ready to feed a million people for a month.
"Our concern is that we get to the people, that people can get out safely, we are ready with food, with anything to help, but we are extremely concerned about the situation."
Mosul residents have reported IS militants are preventing people from getting out.
They report IS is directing some towards buildings they have recently used themselves and which are likely to be targeted by air strikes.
There are fears civilians could also be caught up in chemical attacks, a weapon used by the militants in the past.
The International Committee of the Red Cross has called on all sides in the battle to spare civilians.
The regional director for the Near and Middle East, Robert Mardini, says the world is watching and the combatants must show humanity.
"It means not targeting civilians. It means not targeting civilian infrastructure. It means not attacking medical facilities and medical personnel. It means avoiding the use of heavy explosive weapons in densely populated areas."
Amnesty International says Iraqi authorities must ensure civilians fleeing Mosul are not subject to abuses or revenge attacks by paramilitary and government forces.
The human rights group says Sunni Arabs escaping IS-controlled territory have been tortured, arbitrarily detained and killed by predominantly Shiite militias in the past.
A researcher on Iraq at Amnesty International, Diana Eltahawy, says the Iraqi government cannot be allowed to ignore it.
"These kinds of abuses have been happening for years in a climate of impunity without anyone being punished. The Iraqi authorities really need to translate their calls for the protection of civilians into concrete actions on the ground."
United States president Barack Obama says the safety of civilians is a top priority for the US-led coalition backing the offensive against IS, also known as ISIL.
"Mosul will be a difficult fight, and there will be advances, and there will be setbacks. But I am confident that, just as ISIL has been defeated in communities across Iraq, ISIL will be defeated in Mosul as well, and that will be another step towards their ultimate destruction."
Australia is part of the coalition supporting Iraqi security forces in the offensive on Mosul.
Foreign Minister Julie Bishop has told Sky News taking back the city is an important milestone in the war against IS.
"We understand that it will take some time. The Australian Defence Force has been involved in training and advising and assisting the Iraqi security forces. In fact, we have trained about 12,000 of the security forces, some of whom are taking part in the Mosul offensive now."
