A major military operation in Iraq to retake the Islamic State-held city of Ramadi was under way Tuesday, as fighting and airstrikes were reported west and south of the city.

"Shaping" operations ahead of the counteroffensive began Tuesday, in the form of air strikes, artillery and rocket barrages to rush ISIS out of Ramadi, the Pentagon confirmed. 

Pentagon Spokesman Col. Steve Warren said they welcomed the news of the counteroffensive. 

A spokesman for Iraq's Shiite militias said Tuesday the operation would "not last for a long time" and that Iraqi forces have surrounded Ramadi from three sides, according to The Associated Press.

The Pentagon could not confirm reports that Iraqi security forces had surrounded Ramadi.  

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Warren said Iraqi security forces and Shia militias have staged 20 miles east of Ramadi in the town of Habbaniyah.

New weapons are being used in the battle "that will surprise the enemy," Ahmed al-Assadi, who is also a member of Iraq's parliament, told reporters. He added there was also another operation under way, north of the nearby province of Salahuddin.

According to plans, forces fighting in Salahuddin would surround Ramadi from its northeastern side, he added.

The Anbar province operation aims at cutting off supply routes and recapturing the outskirts of Ramadi first -- not the city itself, according to provincial councilman Faleh al-Issawi and tribesman Rafie al-Fahdawi.

The two told The Associated Press that there was ongoing fighting and airstrikes west and south of Ramadi on Tuesday, adding that more Sunni fighters will be armed starting from Wednesday to join the battle.

Assadi said the code name for the mission is "Labaik ya Hussein,” a slogan in honor of the grandson of the Prophet Muhammad who was killed in the 7th century battle that spawned the rift between Sunni and Shiite Muslims, Reuters reports.

The operation is backed by Shiite militias and Sunni pro-government fighters, the Iraqi state TV reported, without providing further details.

ISIS seized large parts of Anbar in early 2014 and captured Ramadi earlier in May — a fall that marked a major defeat for Iraqi forces, which had been making steady progress against the extremists over the past months with the help of U.S.-led airstrikes.

The operation comes just days after U.S. officials, including Defense Secretary Ash Carter, criticized the Iraqi forces, saying their men fled the Islamic State advance on Ramadi without fighting back, leaving behind weapons and vehicles for the extremists.

But Baghdad defended its troops and quickly said military preparations were under way to launch a large-scale counteroffensive in Anbar, involving Iranian-backed Shiite militias. That possibility sparked fears of potential sectarian violence in the Sunni province, long the scene of protests and criticism against the Shiite-led government in Baghdad.

Security forces and Sunni militiamen who had been battling the extremists in Ramadi for months collapsed as ISIS fighters overran the city.

The militants gained not only new territory 70 miles west of Baghdad, but also large stocks of weapons abandoned by government forces as they fled.

Carter said Sunday that Iraqi forces had "vastly outnumbered" the ISIS militants in Ramadi, but "showed no will to fight."

Saad al-Hadithi, a spokesman for Iraq's Prime Minister Haider al-Abadi, said the government was surprised by Carter's remarks, and that the defense secretary "was likely given incorrect information."

Al-Abadi had called on Shiite militias to help Iraqi troops retake the Sunni province. The militiamen have played a key role in clawing back territory from ISIS elsewhere in Iraq, but rights groups and Sunni residents have accused them of looting, destroying property and carrying out revenge attacks — especially after government forces recaptured the city of Tikrit early last month. Militia leaders deny the allegations.

The participation of the Shiite militias, known as Popular Mobilization Units, in the operation in the Sunni Anbar risks exacerbating sectarian tensions as some of the militias took part in retaliatory sectarian killings that roiled Iraq in 2006 and 2007.

Distrust of the Shiite-led government runs deep in the Sunni Anbar province, where U.S. troops fought some of their bloodiest battles since Vietnam and only succeeded in rolling back militants when Sunni tribesmen and former insurgents rallied to their side as part of the Sahwa, or Awakening, movement beginning in 2006.

After the U.S. troops' withdrawal, the government has largely ignored the Sahwas, and Sunni anger at Baghdad has steadily grown.

The Associated Press contributed to this report.