Ramadi represents a key battle for Iraqi forces. The capital of Anbar province, it is the largest population centre they have tried to retake from Isis.
Backed by US air power, the offensive also marks the Iraqi armed forces' first major battle from which Shia militias have been largely excluded, testing whether the military can go it alone.
"We've entered the centre," said Brigadier General Hamid al-Fatlawi, commander of the Iraqi Army's 8th Division. Iraqi forces have encountered "simple" resistance from the militants, he said.
Intercepted Isis communications in recent weeks had shown that the militants were increasingly desperate, with leaders imploring their fighters to stay and resist. The US military estimates that just a few hundred fighters remain.
Major General Ismail Mahlawi, head of the Anbar Operations Command, said Isis fighters were acknowledging that they had "lost control" and were fleeing to the Isis-controlled town of Hit, 48km to the northwest.
Mahlawi said he expected victory within 48 hours. But despite progress yesterday, much of the city's centre remained in the hands of the extremists.
Iraqi commanders have said they believe they can completely retake the city by year's end.
"We are very optimistic that we will achieve victory in the next few days, because we are already in the centre," said Brigadier General Yahya Rasoul Abdullah, a spokesman for the Iraqi military.
However, he said the large numbers of roadside bombs and snipers made the battle difficult to predict.
Iraqi forces reported progress on several fronts.
In a recent interview, Lieutenant General Abdul Ghani al-Asadi, the head of Iraq's special forces, said he expected it would take around 10 days to clear the city after his forces crossed the river.
The recapture of Ramadi would represent the latest in a string of defeats for the militants and provide a much-needed confidence boost for Iraq's military.
However, Iraqi forces have been heavily reliant on US airstrikes as they slowly reclaim territory from the militants.
Many commanders blamed a lack of US air support for the city's fall in May, when a multipronged car bomb attack caused the collapse of the troops that had withstood Isis attacks for a year and a half.
- Bloomberg