Baghdad — Iraq's Shiite militias on Tuesday launched an offensive intended to put a stranglehold on Islamic State fighters in Ramadi, taking the lead from Iraqi security forces that lost the western city to the extremists just over a week ago.

The operation to cut supply lines and besiege the city from the northeast is "led and managed and planned" by Iraq's popular mobilizations units, a loose formation of Shiite militia groups and volunteers, said Ahmed al-Assadi, a spokesman for the units. There is "coordination and cooperation" with other military forces, he said.

Iraqi Prime Minister Haider al-Abadi had initially held back from sending the Shiite militias to the western province of Anbar, of which Ramadi is the capital, amid sensitivities over dispatching them to a majority Sunni area. Local Sunni tribes, fearing both the Islamic State's advance and potential militia abuses, had been split on whether the Shiite paramilitaries should join the battle.

However, they were ordered to the province last week after the fall of Ramadi highlighted weaknesses in Iraq's regular security forces and the local council requested the militias' assistance. U.S. officials have indicated that they do not object to the mobilization units' involvement in an Anbar offensive as long as they work under the command and control of the Iraqi government.

On a front line in Anbar, where rows of scorched palm trees bore evidence of months of heavy fighting, army soldiers said Monday they had no doubt that the militias were necessary to retake the province.

"Of course we can't fight without the popular mobilization," said Capt. Hussein Najib, an army officer with the Iraqi army's 11th Division who was manning an artillery unit in Garma west of the capital. "The mobilizations are Iraq's unity; they are our right hand."

Their religious fervor is needed in the face of the Islamic State's extremism, added one of his men. "They fight with faith," said 27-year-old Ali Abdulzahra. "We need their energy."

In an indication of the religious overtones of Iraq's war against the Sunni extremists, the offensive to besiege Ramadi has been named "Labayka ya Hussein" — invoking the name of one of Shiite Islam's most revered figures. A Pentagon spokesman, Col. Steve Warren, described the openly sectarian code name as "unhelpful."

The operation, launched early Tuesday, aims to secure the remaining areas in neighboring Salahuddin province, where a fierce battle has raged for the oil refinery in Baiji, before moving on to Ramadi, Assadi said.

"It will finish the liberation of Salahuddin and besiege Ramadi, not liberate it yet," said Assadi. "We expect it will only take a few days, less than a week."

Assadi said militia forces have received new supplies of "modern weapons" that would be used in the battle and "surprise the enemy," but he declined to give further details.

The operation for Ramadi itself would be led by the "sons" of the city, said Moeen al-Kadhimi, an official with the Badr Organization, one of Iraq's most prominent Shiite militias. He said he expected that offensive to be completed within the next two weeks.

The United States and Iraq have traded blame for the fall of Ramadi. Iraqi politicians have hit back at comments by Defense Secretary Ashton B. Carter that Iraqis lacked a "will to fight."

Assadi blamed the United States for failings in the Iraqi military, pointing out the U.S. role in building it after dismantling Saddam Hussein's army in the wake of the 2003 invasion.

"This is the army that you have trained for eight years," he said, addressing the U.S. government. "You worked for eight years and made them weak, through policies that were adopted by you. I say that the Iraqi army, supported by the popular mobilizations, do have the will to fight."

Warren said on Tuesday that the withdrawal from Ramadi was caused by low morale in addition to problems with the command structure. Iraqi forces in the city, including its elite Golden Division fighters, crumbled in the face of multiple car bombs in a nearly four-day offensive by the Islamist militants.