Iraqi government forces are advancing into the centre of the city of Ramadi, which is controlled by jihadist group Islamic State (IS), officials say.
Security sources told the BBC that troops and allied tribesmen, backed by air strikes, had already retaken two districts, and entered two others.
They were heading towards the main government complex, and had 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 their strongholds elsewhere in Anbar province and in neighbouring Syria.
Iraqi Counter-Terrorism Service spokesman Sabah al-Numani said troops from the elite force, supported by the army and police, had begun the assault on central Ramadi at dawn and were advancing towards 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.
Mr Numani added that the counter-terrorism forces had not faced strong resistance, “only snipers and suicide bombers, and this is a tactic we expected”.
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.