Ramadi has been under the control of the extremists since May, when it fell despite an ongoing U.S.-led air campaign in support of Iraqi troops. Backed by intensified airstrikes, Iraqi forces have encircled the city in recent weeks in an offensive that is seen as a key test of their ability to recapture urban areas from the Islamic State.

Much of the city’s center remains in the hands of the extremists, with booby traps and remaining civilians likely to hamper progress. Iraqi commanders, however, have said they believe they can retake it by the end of the year.

The attacking Iraq forces advanced Tuesday from the south of Ramadi, where counterterrorism forces have been leading the fight but had run up against the Euphrates River that bisects the city.

All of Ramadi’s eight bridges have been destroyed in the fighting. On Monday, Prime Minister Haider al-Abadi thanked military engineers for completing a temporary bridge that allowed troops to cross into the city.