The Iraqi army is facing fierce resistance and counter-attacks as it attempts to storm Falluja, a bastion of so-called Islamic State (IS), the BBC reports.
The army’s dawn offensive came a week after it began efforts to retake the city, just 30 miles (50km) west of Baghdad and held by IS since 2014.
An estimated 50,000 civilians are trapped inside, with only a few hundred families escaping so far.
Meanwhile IS militants launched a wave of bombings in and around Baghdad.
The attacks in the Iraqi capital killed at least 21 people.