Iraqi ground forces stormed Ramadi on Tuesday in an attempt to wrest control of the Iraqi city from the Islamic State, which has controlled it for months.

The troops began their offensive Monday night on the edges of the city, and by midday Tuesday had advanced to its center, according to news reports from journalists on the ground.

The offensive was backed by airstrikes from the U.S-led coalition fighting the Islamic State. The troops numbered up to 10,000 men, and included Iraqi government troops and U.S.-trained counterterrorism forces, according to The Wall Street Journal, as well as Sunni tribal fighters, according to The New York Times.

A spokesman for the U.S.-led coalition, Colonel Steve Warren, told the Journal that U.S. intelligence estimates that only about 250 to 350 Islamic State fighters remain in Ramadi, down from about 600 to 1,000 fighters. Officials told news organizations that they believe Iraqi troops could clear out Islamic State militants and take control of the city in a matter of hours.

The Islamic State, which controls about one-third of Iraq and parts of Syria, seized Ramadi from Iraqi forces in May. The government in Baghdad has launched several ultimately unsuccessful offensives to retake the city since July. But earlier this month, Iraqi forces retook Tamim, a large neighborhood on the southwestern outskirts of Ramadi, as well as a key Islamic State operations center there.

Reuters reported that Iraqi military planes dropped leaflets over Ramadi on Sunday that warned residents to leave the city within 72 hours, advised them to carry proper identification, and provided safe routes out.

Local forces have made gains against the militant group elsewhere in Iraq in recent months. In October, Iraqi forces and Shiite militias recaptured most of the country’s largest oil refinery in Baiji. In November, Kurdish and Yadizi forces pushed militants out of Sinjar, which had been under Islamic State control since August 2014.

President Obama said last week that the Islamic State has lost 40 percent of the territory it once controlled in Iraq this year. Since June, his administration has deployed several hundred American military advisors and special-operations troops to Iraq to help local forces in their fight against the terrorist organization.