The army is counting on the support of Sunni tribes in the region recruited by Prime Minister Nouri al-Maliki to help retake the cities because it does not seem capable on its own, analysts say.
Fallujah, about 60 miles west of Baghdad, where U.S. Marines fought the bloodiest battles of the Iraq war, remains largely in jihadist hands along with much of nearby Ramadi, capital of Anbar province.
Maliki's forces have been besieging Fallujah for more than a month, with no serious attempt to storm the city, newspapers report. Maliki has said he wants to avoid civilian casualties but the city of 300,000 has been shelled to soften it up before a ground assault.
Analysts say that after a year-long crackdown by Maliki's forces, tribal leaders in overwhelmingly Sunni Anbar province have set aside deep-rooted grievances with the Shiite-dominated regime to help Maliki crush the jihadists, possibly because he has promised some political concessions.
Given the increasingly autocratic Maliki's track record of refusing to give the minority Sunnis a stake in running the country, imprisoning their political leaders or driving them into exile, he's now asking them to help him to sort out a crisis for which he is at least partly to blame himself.
The terms of the deals he's making with tribal chiefs, who control thousands of fighters, remain unknown. But Arab diplomats report he's handing out millions of dollars and generous infrastructure projects to sweeten the pot.
He's also providing weapons, a risky undertaking given the disenchantment with the government among the disenfranchised Sunnis, who make up about 30 percent of Iraq's population of 31.8 million.
There is a lot of mistrust on both sides, although many Sunnis do not want to live under jihadist rule in the Islamist emirate al-Qaida wants to establish in Iraq and neighboring Syria, a development that, along with Kurdish aspirations of independence in the north, adds some weight to fears Iraq may eventually disintegrate into sectarian enclaves.
The Sunnis' cooperation with Maliki's forces, whose heavy-handed crackdown gave al-Qaida the opportunity to seize territory and raise their black banners over Fallujah and Ramadi in the first place, has two main objectives.
Those goals are "containing a resurgent al-Qaida, and establishing a basis for reconciliation talks with Maliki's Shiite-dominated government," Oxford Analytica said.
"However, while the pragmatic alliance between Sunni tribes and Maliki's security forces could provide the catalyst for much-needed reconciliation initiatives, its collapse could equally lay the ground for further sectarian escalation."
Al-Qaida was effectively crippled by U.S. forces several years ago. But since the Americans withdrew in December 2011, jihadists of the Islamic State of Iraq and the Levant, al-Qaida's Iraqi wing, have been able to rebuild their strength because Maliki's army and security forces have proved incapable of smashing them without U.S. support.
Right now, Maliki desperately needs a military victory in Anbar province if he has any expectations of winning parliamentary elections scheduled for April, in which he's seeking a third term.
He barely scraped home in the 2010 poll. If he can't recapture Fallujah and Ramadi, even his supporters among Iraq's Shiite majority could dump him.
Meantime, al-Qaida's campaign of violence, largely directed against Shiites, escalates as the jihadists seem to be trying to stretch Baghdad's army as thinly as possible.
While Maliki's been concentrating his forces in Anbar, the bloodletting's intensified in the restive northern cities of Mosul and Kirkuk.
There's been a resurgence of execution-style killings in Baghdad, once a mixed city but now controlled by Shiites, many of them installed in neighborhoods that once were Sunni.
"The greatest danger at the moment is that the focus on Anbar and Fallujah is tying up Iraqi military resources, giving ISIL a freer hand in other parts of the country," analyst Marc Simms of Geopolitical Monitor said.
"Even if the loyalists triumph in Anbar, the pattern is set for sectarian militias playing a predominant role in Iraqi politics at the expense of a representative and unified state. ...
"Maliki could always seize the initiative and create a more representative military force, but unfortunately history does not give much cause for hope."
Notable deaths of 2014 [PHOTOS]