Iraqi forces are advancing into the centre of Ramadi, after launching a major assault to drive Islamic State (IS) from the city, officials say.
Security sources said that troops and allied tribesmen, backed by US-led air strikes, had already retaken two districts, and entered two others.
They are heading towards the main government complex, and have come up against snipers and suicide bombers.
Ramadi fell to IS in May in an embarrassing defeat for the Iraqi army.
Last month, government forces completed their encirclement of the predominantly Sunni Arab city, about 90km west of Baghdad, cutting off jihadists inside the centre from strongholds elsewhere in Anbar province and in neighbouring Syria.
Iraqi Counter-Terrorism Service spokesman Sabah al-Numani said its troops, supported by soldiers, police and Sunni tribesmen, had begun the assault on central Ramadi at dawn and were advancing on the government complex.
"We went into the centre of Ramadi from several fronts and we began purging residential areas," he told the AFP news agency.
"The city will be cleared in the coming 72 hours."
"We did not face strong resistance - only snipers and suicide bombers, and this is a tactic we expected," he added.
Sources in the Iraqi military told the BBC that engineers had built temporary bridges over the River Euphrates, which flows along the north and west of the city centre. This had enabled troops to enter directly the al-Haouz district, south-west of the government complex.
A spokesman for the US-led coalition against IS, which carried out at least 12 air strikes in support of the offensive on Tuesday, said the fall of Ramadi was "inevitable", but warned that it would be a "tough fight".
Col Steve Warren suggested there were between 250 and 350 IS militants entrenched in the city centre, with some hundreds more to the north and west.
The Iraqi defence ministry said the jihadists had prevented civilians leaving Ramadi since leaflets warning of an assault were dropped over the city last month.
"They plan to use them as human shields," spokesman Naseer Nuri said.
There are reportedly still thousands, possibly tens of thousands, of civilians inside Ramadi.
Sources inside Ramadi told the BBC that IS had carried out a campaign of raids and mass arrests of residents in districts still under its control, in an attempt to prevent an uprising in support of the government offensive.
The operation to recapture Ramadi, which began in early November, has made slow progress, mainly because the government has chosen not to use the powerful Shia-dominated paramilitary force that helped it regain the northern city of Tikrit to avoid increasing sectarian tensions.
IS has lost control of several key towns in Iraq to government and Kurdish forces since overrunning large swathes of the country's west and north in June 2014 and proclaiming the creation of a "caliphate" that also extended into neighbouring Syria.
On Monday, analysis by IHS Jane's suggested that IS had lost 14 percent of its overall territory in Iraq and Syria, about 12,800 sq km over the past year.
Despite this, the group has been able to capture new territory of strategic value over the same period, including Ramadi and Palmyra in Syria's Homs province. It also still controls the Iraqi cities of Falluja, east of Ramadi, and Mosul, in the north.