Iraqi forces are advancing into the centre of Ramadi, after launching a major assault to drive Islamic State militants from the city, officials say.
Security sources told the BBC 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 (55 miles) west of Baghdad, cutting off militants 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's Anbar Operations Command 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.
By Tuesday afternoon, government forces had retaken the al-Thubat and al-Aramil districts, and entered nearby al-Malaab and Bakir, the sources said.
Sunnis to the fore - Lina Sinjab, BBC News, Beirut
If the battle to recapture Ramadi succeeds, it will be the second-largest city after Tikrit to be taken back from the self-proclaimed Islamic State in the past 18 months. It would be a major boost for the morale of the Iraqi security forces and for those Sunnis opposing IS in Iraq.
That is not only because the city of Ramadi is predominantly Sunni and a key IS stronghold, but also because the forces fighting to take it back are spearheaded by Sunni tribesmen.
The Shia-dominated paramilitary force known as Popular Mobilisation (al-Hashd al-Shaabi) has been involved in many battles against IS, but the government has chosen not to deploy it in Ramadi.
The force was accused of human rights abuses against Sunnis after the recapture of Tikrit in April, and it is believed previous atrocities carried out by Shia militias helped alienate Sunnis and push them into the arms of IS.
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 told the Reuters news agency on Monday.
Col Warren said there were still thousands, possibly tens of thousands, of civilians inside Ramadi.
Sources inside Ramadi told the BBC 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.
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% of its overall territory in Iraq and Syria, about 12,800 sq km (4,940 sq miles), 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.
What is Islamic State?
A notoriously violent Islamist group which controls large parts of Syria and Iraq. It has declared its territory a caliphate - a state governed in accordance with Islamic law - under its leader Abu Bakr al-Baghdadi.
What does it want?
IS demands allegiance from all Muslims, rejects national borders and seeks to expand its territory. It adheres to its own extreme interpretation of Sunni Islam and regards non-believers as deserving of death.
How strong is IS?
IS projects a powerful image, partly through propaganda and sheer brutality, and is the world's richest insurgent group. It has about 30,000 fighters but is facing daily bombing by a US-led multinational coalition which has vowed to destroy it.