UN officials have received "credible reports that families are being concentrated into the center of the city by Daesh and they are not allowed to leave these concentration points," said UN deputy representative to Iraq Lise Grande, using a term for the IS group.
"That would suggest that Daesh could be using them or may intend to use them as some kind of human shield," she told reporters.
"They are at extreme risk if there is a military confrontation."
Iraqi forces launched an offensive a week ago to recapture Fallujah, which became an IS group stronghold after its fighters seized the city in January 2014.
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The United Nations has raised concerns with the Iraqi government, which has slowed down the pace of its operation to try to protect the trapped families.
The government is "fully aware" of the need to protect civilians during the assault, Grande said.
"The operation is moving more slowly than it might otherwise," she added.
Only 5,000 civilians of the 50,000 trapped in the city have managed to escape, many of whom walked for hours and came under fire as they fled, Grande said.
Fallujah and Mosul -- the capital of the northern province of Nineveh -- are the last two major cities the IS group holds in Iraq.