The operation, which involved police, pro-government militiamen and SWAT forces, sought to wrest back key neighbourhoods of Ramadi, the capital of Anbar province and one of two cities where the authorities lost vast swathes of territory about three weeks ago.
It came as Jordan said it would host a US training programme for Iraqi forces grappling with the country's worst bloodshed since 2008 and the ongoing deadly standoff in Anbar which have combined to leave more than 650 people dead so far this month.
Iraqi troops, policemen, SWAT forces and tribal fighters moved into five neighbourhoods of Ramadi on Sunday, with helicopters providing them cover and firing on targets in the sprawling Malaab district that has been at the centre of fighting between anti-government fighters and security forces and their tribal allies.
"The Iraqi army launched a large operation with helicopter cover against Daash, Al-Qaeda and terrorists in Ramadi," defence ministry spokesman Staff Lieutenant General Mohammed al-Askari said, according to state television, employing terms frequently used by the Iraqi security forces to describe militants.
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All of the neighbourhoods targeted lie in the south or centre of the city.
The operation will seek to take back momentum from anti-government fighters, who have expanded their hold on Ramadi in the past week after police and allied tribesmen trumpeted gains there earlier this month.
A large section of Ramadi and all of Fallujah, both former insurgent bastions close to Baghdad, fell from government control late last month.
It was the first time anti-government fighters have exercised such open control in major cities since the height of the insurgency that followed the US-led invasion of 2003.
It spread to Fallujah, and militants moved in and seized the city and parts of Ramadi after security forces withdrew.
Iraqi Prime Minister Nuri al-Maliki told The Washington Post in an interview published on Thursday that Baghdad specifically needed US "counter-terrorism" training.
The US defence official said Washington was also preparing to ship "several thousand" M-16 and M-4 assault rifles as well as ammunition to Iraq, after having already provided missiles to Maliki's government.