Iraqi police say government forces have recaptured more than 90 percent of Ramadi from ISIL militants.
The US-led coalition is carrying out air strikes across the region, while specially-trained anti-terror troops have been moving street-by-street on the ground to force out the jihadists.
Ramadi, the capital of the vast Anbar Province, lies just over 100 kilometres west of Baghdad.
Its fall to ISIL in May was a major blow to a government struggling to claw back territory from the group.
The advance has been slow, with security forces hindered by snipers and suicide bombers.
However, Iraqi officials say the operation marks the most significant progress made by the military in seven months and they hope to have full control over the city by the end of the week.
If they are successful, it will be the second major city to be retaken from the militants after Tikrit.
While Iraqi officials are optimistic the recapture of Ramadi will be swift, the US coalition was more cautious.
Spokesman Colonel Steve Warren earlier estimated up to 350 ISIL fighters remained in the city.
Analysts suggest ISIL has lost 14 percent of its territory across Iraq and Syria in the past year. But, it has managed to hold on to Mosul, Iraq’s strategically-important second city.
Get a different perspective
Every story can be told in many ways: see the perspectives from Euronews journalists in our other language teams.