Last Updated May 26, 2015 3:13 PM EDT
BAGHDAD -- Iraq has announced the launch of an operation to drive the Islamic State of Iraq and Syria (ISIS) out of the western Anbar province, where the extremists captured the provincial capital earlier this month.
CBS News correspondent Holly Williams reports parts of Anbar province have been under ISIS control for more than a year, and thousands of people continue to flee the city following the fall of the provincial capital, Ramadi.
Iraq's media, citing police in Anbar, announced the Ramadi counteroffensive, saying the attack would take place on three fronts. Anbar Police chief General Hadi Kassar said Iraqi army and police forces, backed by 5,000 Shiite militiamen, were taking part in the operation. Iraq's air force appeared to be providing cover, with at least one strike reportedly killing a handful of ISIS militants near Ramadi.
Military sources said the attack on three fronts was aimed at cutting off ISIS supply routes into the city.
A Pentagon spokesman said Tuesday that Iraqi forces have begun "shaping operations" and "security zone interactions," describing them as probing and reconnaissance actions that would precede any major combat against ISIS in or around Ramadi .
Col. Steve Warren said the Iraqis have begun moving forward from their base in the province's town of Habbaniyah and that ISIS fighters are also probing in the direction of the town. Warren said he could not confirm that the Iraqi forces have surrounded Ramadi.
ISIS seized large parts of Anbar starting in early 2014 and captured Ramadi about 10 days ago. The fall of Ramadi marked a major defeat for Iraqi forces, which had been making steady progress against the extremists over the past year with the help of U.S.-led airstrikes.
The announcement that the operation to reclaim Anbar had begun came a day after Iraqi Prime Minister Haider al-Abadi refuted accusations from a senior Obama administration official that his troops lacked "the will to fight" ISIS, and essentially gave up Ramadi without a fight.
Speaking to BBC News just hours after U.S. Secretary of Defense Ash Carter made those remarks, al-Abadi said he was "surprised" to hear such a key figure in Washington blast the Iraqi troops' efforts, noting Carter had been "very supportive of Iraq."
"I'm sure he was fed with the wrong information," al-Abadi told the BBC, without clarifying which of Carter's claims, specifically, he was rejecting.
But while al-Abadi said the loss of Ramadi made his "heart bleed," he insisted it would be a short-lived victory for the Sunni extremists.
"I can assure you we can bring it back (under government control) soon," he said of Ramadi. "I'm talking about days."
There have been serious concerns, however, that the outsized role Iran-backed Shiite militias are expected to play in the government offensive in predominantly Sunni Anbar province could stoke the flames of Iraq's sectarian tensions.
Many Iraqi Sunnis -- who were the ruling minority under Saddam Hussein -- harbor a deep distrust of the nation's majority Shiites, and the Shiite militias in particular, which have been accused of committing atrocities including the execution of Sunni civilians in other areas where they've helped to oust ISIS.
Almost immediately, fears that the offensive in Anbar could take on a sectarian overtone were highlighted by a proclamation from a spokesman for the Shiite militias, who appeared on television to assert leadership of the operations -- and give them a name that, in and of itself, was sure to anger Sunnis.
According to the Reuters news agency, the militia spokesman dubbed the offensive "Labaik ya Hussein," a tribute to the grandson of the Prophet Muhammad, whose 7th century death on the battlefield sparked the rift between Sunni and Shiite muslims.
"The Labaik Ya Hussein operation is led by the Hashid Shaabi (Shiite militias) in cooperation and coordination with the armed forces there," Assadi said, according to Reuters. "We believe that liberating Ramadi will not take long."
That confidence, echoing Prime Minister Hadi's Monday prediction of victory within "days," seems optimistic to CBS News senior national security analyst Juan Zarate.
Zarate said the rapid military response to the fall of Ramadi seemed to be largely a "face-saving" exercise by officials in Baghdad.
"They realize that this is a major setback, psychologically damaging to their forces and internationally, and so they have to announce something. Whether or not this is possible in the near term is really to be seen, but I think it's going to be a real challenge to take back Ramadi, just like it's been a challenge to take back other territory from the Islamic State."