The drive to recapture the first city to be lost from government control in 2014 came as fighting also raged in neighbouring Syria, leaving huge numbers of civilians exposed.
Led by the elite counter-terrorism service (CTS), Iraq's best trained and most seasoned fighting unit, the forces pushed into Fallujah before dawn, commanders said.
"Iraqi forces entered Fallujah under air cover from the international coalition, the Iraqi air force and army aviation, and supported by artillery and tanks," said Lieutenant General Abdelwahab al-Saadi, the commander of the operation.
"There is resistance from Daesh," he added, using an Arabic acronym for IS.
CTS spokesman Sabah al-Noman told AFP: "We started early this morning our operations to break into Fallujah."
The involvement of the elite CTS marks the start of a phase of urban combat in a city where in 2004 US forces fought some of their toughest battles since the Vietnam War.
The week-old operation had previously focused on retaking rural areas around Fallujah, which lies just 50 kilometres west of Baghdad.
They were still in action today, attempting to clear an area northwest of Fallujah called Saqlawiya, officers said.
Only a few hundred families have managed to slip out of the Fallujah area ahead of the assault on the city, with an estimated 50,000 civilians still trapped inside, sparking fears the jihadists could try to use them as human shields.
The only families who were able to flee so far lived in outlying areas, with the biggest wave of displaced reaching camps on Saturday night.
"We expect bigger waves of displacement the fiercer the fighting gets."
In Amriyat al-Fallujah, a government-controlled town to the south of the jihadist bastion, civilians trickled in, starving and exhausted after walking through the countryside for hours at night, dodging IS surveillance.
Fallujah is one of just two major urban centres in Iraq still held by IS jihadists.
