Since the beginning of the US-backed Iraqi forces' advance three weeks ago, the fighting has displaced "just over 33,000 people," a US official said in a conference call with reporters.
"That is lower than initially expected, but it's important to keep in mind that the Iraq security forces still have not reached the most populous areas."
At least one million people are believed to be trapped by the fighting, but it is impossible to verify the number in a city under the IS group's control since June 2014.
The United Nations, the Iraqi government, nonprofit organizations and the US government have mounted a massive effort to help those displaced by the fighting.
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Some 50 trucks a day have been bringing food and other supplies to the Mosul region for the past several weeks to prepare for a flood of displaced people, the official said.
Humanitarian agencies estimate as many as 700,000 people will flee the fighting.
Camps for the displaced currently have 80,000 places ready, with the aim of preparing a total of 250,000 by mid-December, US officials told reporters.
"This situation may be one of the best-prepared responses to a humanitarian emergency... that we have seen certainly in a long time," another US official said on the call.
Some of those displaced by the Mosul fighting will find shelter with relatives and not need to go to the camps, humanitarian groups say.
Around half of the displaced have found their own shelter so far, US officials said.