Iraqi forces have entered Falluja - and are encountering little resistance from ISIS
The Iraqis also besieged the city's main hospital, accoring to the New York Times' Baghdad bureau chief, Tim Arango.
"ISIS has lost its power to defend Falluja," Col. Jamal Lateef, a police commander in Anbar Province, told the Times. "Its defensive lines have collapsed, and the battle of Falluja will be over in no time."
The ultra-hardline militants still control a significant portion of the city, however, where the conflict has forced the evacuation of most residents and many streets and houses remain mined with explosives.
But the Times reported that the jihadists abandoned their positions and put a minimal fight against the Iraqi army.
"ISIS has collapsed in Falluja very fast," Lt. Gen. Adbulwahab al-Saadi, a commander of Iraq's counterterrorism forces who is in charge of the Falluja operation, told the Times.
Iraqi special forces, along with the army, Shi'ite Muslim militias, Sunni tribal fighters and U.S.-led coalition air strikes, launched a major operation on May 23 to retake Falluja, an historic bastion of the Sunni insurgency against U.S. forces that toppled dictator Saddam Hussein, a Sunni, in 2003, and the Shi'ite-led governments that followed
The city, which fell to ISIS in 2013, is seen as a launchpad for Islamic State bombings in the capital, making the offensive a crucial part of the government's campaign to improve security. U.S. allies would prefer to concentrate on Islamic State-held Mosul, Iraq's second largest city in the far north.
Thousands of civilians have fled Falluja since the fighting began in late May. Many were shot by ISIS while trying to escape, while others were forced to remain in the city to serve as human shields for the militant group.