"The liberation must be followed by genuine dialogue leading to a compromise among all components of Iraqi society in order to ensure sustainable peace for the future," Xinhua news agency quoted UN spokesman Stephane Dujarric as saying at a news briefing on Tuesday.
He added that reports on the first 36 hours of the military operations in Iraq indicate that military activities on the ground have taken place in less populated areas and are not leading to immediate large scale displacements of affected people.
"No significant civilian displacement out of Mosul has been recorded so far," he said.
"Serious concerns remain for the protection of civilians as hostilities intensify closer to and in densely populated and urban areas," he said.
An estimated 200,000 people are anticipated to be displaced in the coming weeks of the offensive.
"Preparations are focusing on identification, assessment and establishment of displacement sites to receive displaced families. Continuous monitoring of civilian displacement is taking place," he said.
Mosul, some 400 km north of the Iraqi capital of Baghdad, has been under IS control since June 2014, when Iraqi government forces abandoned their weapons and fled, enabling IS militants to take control of parts of Iraq's northern and western regions.