The figure increased significantly over the past week as forces battled deep into the densely populated city, but it falls short of pre-offensive predictions.
"68,550 people are currently displaced and in need of humanitarian assistance," the United Nations' Office for the Coordination of Humanitarian Affairs said in a statement reported by AFP.
OCHA said the aid response to the offensive launched against the extremists on Oct. 17 was growing in complexity, with varying needs for different categories of civilians.
"Humanitarian needs are severe among displaced families in and out of camps, vulnerable residents of retaken communities, and people fleeing the intense fighting in Mosul city," it said.
A million-plus civilians were thought to still live inside Mosul, the country's second city and the extremists' last major bastion in Iraq, before the operation was launched.
The UN had initially predicted that 200,000 civilians could be forced from their homes in the first few weeks of the offensive, Iraq's biggest military operation in years.