Iraqi government forces are fighting Islamic State militants near Falluja and bombarding central districts, as an offensive begins to retake the longtime jihadist stronghold that sits a short drive from the capital Baghdad.  

Iraqi forces have had the city surrounded since last year.

But overnight, air strikes and mortar salvoes targeted suspected IS headquarters in the heart of the city, the aim being to weaken resistance for ground troops to enter.

But a military spokesman says the army is taking great care - with roadside bombs littering the approach roads, planted by some of the several hundred militants occupying Falluja.

Abadi announced the offensive in a late-night televised speech.

He's exchanged his usual suit for the black uniform of an elite commando unit, overseeing operations at a command center near Falluja.

The city was the first to fall to Islamic State in Iraq as it swept through the area to create its own caliphate.

Two-thirds of its population has fled. Those who remain are believed to be living in dire conditions.

But Abadi says the time has come to retake Falluja, and restore it to Iraqi government control.