Iraq's army chief has been quoted as saying he needs only days to drive Islamic State from the city of Ramadi.
Ramadi's fall in May exposed the weakness of the Baghdad government and dampened hopes of restoring control in the north and west.
Iraqi troops began advancing on Tuesday in an offensive complicated by rivalries and suspicions harboured by local Sunni tribes and by Shia militia backed by Iran. US officials, concerned also by militant operations over the border in Syria, have expressed frustration at delays in seizing back the city.
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"In the coming days will be announced the good news of the complete liberation of Ramadi," Iraqia TV cited army chief of staff Lieutenant General Othman al-Ghanemi as saying on Wednesday.
Government troops are now concentrating on the last district held by the militants in the centre of Ramadi, a Sunni Muslim city on the river Euphrates some 100 km (60 miles) west of Baghdad and capital of Anbar province.
If it is captured, it will be the second major city after Tikrit to be retaken from Islamic State in Iraq. It would provide a major psychological boost to Iraqi security forces after the militant group seized a third of Iraq, a major OPEC oil producer and U.S ally, in a sweeping advance last year.
Progress has been slow because the government wants to rely entirely on its own troops and not use Shi'ite militias in order to avoid rights abuses such as occurred after the recapture of Tikrit from the militants in April.
Iraqi officials say Shi'ite militias are reluctant to yield power amassed with Iranian backing, making it hard to forge a unified strategy. Operations are also complicated by competition for influence in Baghdad between Washington and Tehran.
Local Sunni tribes have not been involved directly in the assault, but have been active in support activities across the province - a contrast to the US-backed Tribal Awakening campaign ten years ago when they united to drive al Qaeda elements from Anbar.
Joint operations command spokesman Yahia Rasool told Reuters the city would be handed over to the Anbar police and local tribes after it was fully cleared and secured.
By contrast to 2005, the Sunni tribes are now dealing with a government less given to sectarian Shia loyalties.
The ultimate aim is to clear Islamic State from Mosul, Iraq's second largest city, and Falluja, which lies between Ramadi and Baghdad, as well as large areas of Syria - the core of what it has declared to be a caliphate.
The control of major population centres in Iraq and Syria allows it to maintain a revenue base, controlling oil resources and large, fertile agricultural areas, and possibly plan attacks outside its core territory.
Citing military statements, state TV said government forces had killed hundreds of militants since Tuesday. It gave no casualty toll for government forces.
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