"Great people, the hour of victory against the Daesh criminal gangs (IS) has come," said a statement from the Joint Operations Command for Anbar province, of which Ramadi is the capital.
"Your heroic forces are advancing steadily from the northern side... They managed to reach Albu Farraj area," on the northern edge of the city centre, it said.
The head of the Anbar command, Major General Ismail Mahalawi, told AFP that "Iraqi forces have raised the Iraqi flag on Albu Farraj bridge", over the Euphrates.
IS fighters took Ramadi, about 100 kilometres (60 miles) west of Baghdad, in mid-May after a three-day blitz of massive suicide car and truck bomb attacks that forced a disorderly retreat by pro-government troops.
After the most stinging setback suffered by Iraqi forces since they started a counter-offensive to regain the territory lost in mid-2014, officials vowed to swiftly retake Ramadi.
Progress has been sluggish however, with Iraqi forces and the US-led coalition supporting them in Anbar blaming a number of factors, including searing summer temperatures.
But yesterday he said Iraqi forces were now ready to launch an operation inside the city.
"We now believe that battlefield conditions are set for the ISF (Iraqi security forces) to push into the city," he said, estimating between 600 and 1,000 the number of IS fighters remaining in Ramadi.
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