The effort to win back parts of Ramadi, capital of the western province of Anbar and one of two cities that either entirely or partly fell out of government control weeks ago, comes with violence at its highest level since 2008.
Soldiers and police fought alongside armed pro-government tribesmen in southern Ramadi in some of the heaviest clashes of recent weeks, a police officer and an AFP journalist said.
They were making slow progress in retaking militant-held neighbourhoods as acting Defence Minister Saadun al-Dulaimi visited to oversee operations.
On Saturday the defence ministry announced that warplanes and artillery had hit a neighbourhood of northern Fallujah, a rare military operation inside the city itself.
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The army has largely stayed out of Fallujah, a short drive from Baghdad, fearing major incursions could ignite a protracted conflict with massive civilian casualties and damage to property.
US battles in the city, a bastion of militants following the 2003 US-led invasion, were among their bloodiest since the Vietnam War.
The Al-Qaeda-linked Islamic State of Iraq and the Levant has been involved in the fighting, as have other militant groups and anti-government tribes.
The police and the army have recruited their own tribal allies.
The stand-off has prompted more than 140,000 people to flee their homes, the UN refugee agency said, describing it as the worst displacement in Iraq since the peak of the 2006-2008 sectarian conflict.
The deadliest violence struck in the town of Baiji, where a coordinated attack on an encampment of anti-Qaeda Sunni militiamen, or Sahwa fighters, killed eight people in all, security and medical officials said.
An initial gun attack on the base was followed by a suicide car bomb, with 17 others wounded.
Attacks in the areas of Baghdad, Balad, Taji, Mosul and Kirkuk killed 13 more people.
Violence has spiked markedly in recent months, with more than 1,000 people killed in January, the highest toll for a month since April 2008, according to government data.