"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 in charge of the operation.
"Counter-terrorism service (CTS) forces, the Anbar police and the Iraqi army, at around 4 am (0100 GMT), started moving into Fallujah from three directions," he said. "There is resistance from Daesh," he added, using an Arabic acronym for IS.
CTS spokesman Sabah al-Norman 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 US forces in 2004 fought some of their toughest battles since the Vietnam War.
The week-old operation had previously focused on retaking villages and rural areas around Fallujah, which lies just 50 kilometres (30 miles) west of Baghdad.
Only a few hundred families 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. Fallujah is one of just two major urban centres in Iraq still held by IS. They also hold second city Mosul.