The battle to drive out Islamic State of Iraq and Syria (ISIS) fighters out of the centre of Ramadi is entering its second day as Iraqi special forces fight the militants street by street.
Officials are optimistic that the city will be recaptured by the weekend.
But a spokesman for the US-led coalition has been more cautious, saying a tough fight is in prospect.
Iraqi forces 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.
Security sources told the BBC troops and allied tribesmen, backed by US-led air strikes, had already retaken two districts, and entered two others.
Iraqi Counter-Terrorism Service spokesman Sabah al-Numani said its troops, supported by soldiers, police and Sunni tribesmen, began the assault on central Ramadi at dawn on Tuesday.
