"We are concerned over the protection of children in the face of extreme violence," UNICEF Representative in Iraq Peter Hawkins said in a statement.
"Children face the risk of forced recruitment into the fighting" inside the besieged city, and "separation from their families" if they manage to leave, he added.
Backed by Shi'ite militias and air strikes from the US-led coalition, the Iraqi armed forces launched on May 23 an offensive to recapture Falluja, 50 kms (32 miles) west of Baghdad.
The assault on Falluja has begun what is expected to be one of the biggest battles ever fought against ISIS.
Falluja was the first Iraqi city that fell under control of the Sunni terrorists, in January 2014.
About 50,000 civilians remain in the city, according to the United Nations.
Iraqi security forces operating in Falluja separate systematically men and boys over 12 from the families to probe possible links with ISIS.
"UNICEF calls on all parties to protect children inside Falluja, provide safe passage to those wishing to leave the city and grant safe and secure environment to civilians who fled Falluja," Hawkins said.