The militants seized Falluja in January 2014, six months before they declared a "caliphate" over part of Syria and Iraq
Islamic State has begun allowing thousands of civilians trapped in central Falluja to escape
Falluja would be the third major city in Iraq recaptured by the government after Tikrit and Ramadi
Falluja was the first Iraqi city to fall to Islamic State in January 2014
The attacks came as Iraqi forces and Shi'ite militias are fighting Islamic State militants in Falluja
Clashes involving aerial bombardment, artillery and machine gun fire are continuing.
"As a result, we unfortunately expect an increase in mass casualty attacks and sabotage of economic infrastructure."
Tens of thousands of civilians are trapped in the city with limited access to water, food and healthcare.