75,000 residents remain trapped in DAESH-controlled Fallujah since the city fell to the terrorists in 2014.
Thousands of residents remain trapped as Iraq launched a major offensive to retake Fallujah, one of the last remaining strongholds of DAESH.
Iraqi Prime Minister Haider al-Abadi on Monday said, "In the early hours of the morning today, the heroic fighters advanced from different sides to retake all the areas occupied by DAESH around Fallujah."
Abadi said the operation was supposed to start earlier, but "political problems and also the events... threatening security inside Baghdad delayed some of the preparations".
Fallujah, located 50km west of Baghdad, was the first city to fall to DAESH terrorists in January 2014, but according to the Iraqi premier, "they had no choice but to flee."
In a joint address by the government and the military on Sunday, Abadi said the "moment of great victory" had drawn.
The operation was being conducted by the army, police, counterterrorism forces, local tribal fighters and a coalition of local militias who have surrounded the city for months.
Reports of heavy shelling in the city were trickling in by Monday.
But the fight to retake Fallujah will be complicated by the fact that DAESH has had two years to reinforce their position in the city and with it trapped between 70,000 to 90,000 residents.
PM Al-Abadi announces the launch of operations to liberate Fallujah pic.twitter.com/Mf0KN7MMoq— Haider Al-Abadi (@HaiderAlAbadi) May 22, 2016
The Iraqi military's media unit told residents to leave on Sunday or 'raise a white flag outside their houses' if they remain trapped.
Deputy District Council Chairman Falih al-Essawi said three corridors would be opened for civilians to camps west, southwest and southeast of the city, and a subsequent military statement said some residents had begun to flee.
Perilous journey out
According to Reuters, about 20 families set out from a southern frontline neighbourhood late on Saturday, but only half of them made it out.
Some were intercepted by DAESH, while others were killed by explosives planted along the road.
The United Nations and Human Rights Watch said last month that residents were facing acute shortages of food and medicine during a siege by government forces.
Aid has not reached the city since the Iraqi military recaptured nearby Ramadi in December.
Fallujah is known as the 'City of Minarets' and 'Mother of Mosques' and it was badly damaged in two offensives by US forces against al-Qaeda insurgents in 2004.