Iraqi forces launched a broad operation on Tuesday to tighten the noose on jihadists controlling Anbar, but Shiite militias gave it a name that risked raising sectarian tensions.
Ten days after the Islamic State group's shock capture of the capital of Iraq's largest province, a spokesman said an offensive to cut off Anbar and prepare for a bid to retake Ramadi had begun.
"The operation's goal is to liberate those regions between Salaheddin and Anbar and try to isolate the province of Anbar," said Hashed al-Shaabi spokesman Ahmed al-Assadi.
The Hashed al-Shaabi ("popular mobilisation" in Arabic) is an umbrella group for mostly Shiite militia and volunteers, which the government called in after the Islamic State group (IS) captured Ramadi on May 17.
Assadi said the latest offensive had been dubbed "Operation Labaik ya Hussein", which roughly translates as "We are at your service, Hussein" and refers to one of the most revered imams in Shiite Islam.
The Pentagon, which is also active against IS in Anbar with air strikes, was clearly frustrated with the choice of an explicitly sectarian codename for an operation into Iraq's Sunni bastion.
"I think it's unhelpful," spokesman Colonel Steven Warren said.
"We've long said... the key to victory, the key to expelling ISIL from Iraq is a unified Iraq," Warren said, using an alternative acronym for IS.
Washington had been in favour of keeping the Shiite Hashed forces out of Anbar, but the abysmal performance of the security forces in Ramadi left Prime Minister Haider al-Abadi without other options.
Abadi, who has strived to paint the Hashed as a cross-sectarian force by including Sunni fighters in it, did not immediately comment on the controversy.
Edging closer to Ramadi
The operation launched on Tuesday involves 4,000 men, including from the security forces, heading south from Salaheddin to sever IS supply routes to Anbar.
The jihadists control most of the province and the government holds just a few isolated pockets.
Regular forces and Hashed al-Shaabi paramilitaries also made progress south and west of Ramadi, an army lieutenant colonel told AFP, retaking an area called Al-Taesh.
"The Iraqi security forces and Hashed al-Shaabi have now cut off all supply routes for IS in Ramadi from the south," provincial council member Arkan Khalaf al-Tarmuz said.
Washington on Monday had moved to appease Baghdad after a previous spat with the Pentagon, whose chief accused Iraqi forces of "lacking the will to fight".
Ashton Carter's remarks to CNN were widely perceived as unfair in Iraq, where some forces have put up valiant resistance to IS.
In a call to Abadi, the White House quoted Vice President Joe Biden as saying he "recognised the enormous sacrifice and bravery of Iraqi forces over the past 18 months in Ramadi and elsewhere".
Tehran, main backer of the paramilitary groups sent to Anbar's rescue, was gloating and suggested it was Washington that was indecisive in its approach to IS.
Iraqi fighters from the Shiite popular mobilisation unit fire their weapons in the outskirts of Baiji refinery north of Tikrit.
"How can you be in that country under the pretext of protecting the Iraqis and do nothing? This is no more than being an accomplice in a plot," said General Qassem Suleimani, the Revolutionary Guards' commander of foreign operations.
The US-led coalition has carried out more than 3,000 strikes against IS in Iraq and Syria over the past 10 months.
Baghdad and Washington had boasted that IS was a waning force after months of territorial losses, but Ramadi's fall signalled that the jihadist group may have been written off too soon.
Its seizure of the city prompted 55,000 residents to flee, according to the United Nations.
Many have been prevented from entering provinces, for fear they have been infiltrated by IS.
Some Sunni Arab politicians and activists have described the move as unconstitutional and discriminatory against the minority community.
The International Rescue Committee said the restriction was forcing some people to return to conflict areas.
"Thousands of people fleeing Ramadi are stuck at checkpoints or being denied entry to safe areas," IRC's Syrian crisis response regional director Mark Schnellbaecher said.
"For some people the situation has become so hopeless that they are returning to the conflict in Ramadi."
In a twin attack last week, IS seized Palmyra in eastern Syria and the nearby ruins of the ancient city, considered one of the world's archaeological jewels.
A video posted online by a channel that works only in IS-controlled areas showed the UNESCO-listed site, including its famous theatre and colonnade.
The 90-second undated raw footage also includes a brief shot of a street, in which no IS fighters or flags can be seen.