Around 50,000 people are estimated to still be trapped in the city
Iraqi forces have entered Fallujah under coalition air cover as they start a new phase of their plan to win back one of Islamic State's key cities.
Troops went into Fallujah from three directions backed up by artillery and tanks, commanders told the AFP news agency.
The move was also confirmed to a crew from Reuters - who reported hearing explosions in the city's southern Naimiya district.
"Iraqi forces entered Fallujah under air cover from the international coalition, the Iraqi air force and army aviation and supported by artillery and tanks," Lieutenant General Abdelwahab al-Saadi told AFP.
"Counter-terrorism service (CTS) forces, the Anbar police and the Iraqi army, at around 4am (0100 GMT), started moving into Fallujah from three directions."
The commander said troops were meeting "resistance" from the IS fighters.
Despite many people having fled Fallujah, 50,000 are estimated to still be trapped in the city about 40 miles (65km) west of Baghdad.
The army, backed by an Iranian-backed Shia militia, began the push to take back the city on 23 May and has tightened its grip on the surrounding region.
Fallujah was the first Iraqi city to be captured by Islamic State.
The took control in January 2014, six months before announcing a self-proclaimed caliphate in areas of Iraq and Syria.
Some 500-1,000 IS troops are estimated to be holding the city, with the jihadists reportedly using civilians as human shields and killing people who try to flee.
The Norwegian Refugee Council said it had been "receiving hundreds of displaced Iraqis from the outskirts of Fallujah who are totally exhausted, afraid and hungry".
The city had a population of over 320,000 in 2010 but this has dwindled with the remaining residents caught between the fighting, and enduring food and medicine shortages.
Along with Mosul, Fallujah is one of two major Iraqi cities held by IS.