Parts of Ramadi -- the capital of Anbar province, west of Baghdad -- and all of Fallujah were seized by al-Qaeda-linked militants last week.
It is the first time jihadists have exercised such open control in major cities since the height of the insurgency that followed the 2003 US-led invasion.
"It is not possible to assault (Fallujah) now" due to concerns about civilian casualties, defence ministry spokesman Staff Lieutenant General Mohammed al-Askari told AFP.
And it would be a major test for Iraqi security forces, which have yet to undertake such a major operation without the backing of American forces.
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Overnight, security forces and allied tribesmen sought to retake south Ramadi from fighters loyal to al-Qaeda-linked group the Islamic State of Iraq and the Levant (ISIL), but the assault failed.
"Security forces and armed tribesmen tried last night to enter areas controlled by ISIL fighters in the south of the city," a police captain in Ramadi told AFP.
Four civilians were killed and 14 wounded in the fighting, said Ramadi hospital's Dr Ahmed Abdul Salam, who had no casualty figures for security forces or the militants.
Later today, Iraqi carried out missile strikes against militants in Ramadi, killing 25, Askari said.
Meanwhile, three loud explosions were heard outside Fallujah early Tuesday, a witness said, while the army deployed reinforcements.
"Today, the army sent new reinforcements, including tanks and vehicles, to an area about 15 kilometres east of Fallujah," a police captain told AFP.
But senior tribal leader Sheikh Ali al-Hammad said that ISIL's fighters had left Fallujah, and that it was now in the hands of tribesmen.