Iraqi forces have clashed with fighters of the so-called Islamic State near Fallujah while bombing central districts in the initial hours of an offensive to retake the militant stronghold just west of Baghdad.
Some of the first direct engagement occurred in al-Hayakil area on the city's southern outskirts, a resident said.
Troop salso approached the northern suburb of Garma, the top municipal official there said, to clear out militants before turning attention towards the city centre.
Air strikes and mortars overnight targeted neighbourhoods inside the city proper where Islamic State is thought to maintain its headquarters.
But the bombardment had eased by daylight.
Iraqi military spokesman Brigadier General Yahya Rasool, speaking on state television, described the forces' advance as "careful" and reliant on engineers to dismantle roadside bombs planted by the militants.
Fallujah was the first city to fall to Islamic State, in January 2014.
Six months later, the group declared a caliphate spanning large parts of Iraq and neighbouring Syria.
Iraqi forces have surrounded the city since last year but focused most combat operations on IS-held territories further west and north.
The authorities have pledged to retake Mosul this year in keeping with a US plan to dislodge Islamic State from their de facto capitals in Iraq and Syria.