WASHINGTON — The Pentagon expressed disappointment on Tuesday over a decision by Iraqi militias to impose an explicitly Shiite name for a military operation in Iraq's Sunni heartland, saying it could aggravate sectarian tensions.

An umbrella group for mostly Shiite militia and volunteer fighters, Hashed al-Shaabi, said it had dubbed a military campaign to cut off the Islamic State group in Anbar province as "Operation Labaik ya Hussein," which roughly translates as "We are at your service, Hussein."

The name refers to one of the most revered imams in Shiite Islam.

"I think it's unhelpful," spokesman Col. 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 the IS group.

That required "a unified Iraq that separates itself from sectarian divides, coalesces around this common threat and works to expel ISIL from Iraq," he said.

"The solution is a unified Iraqi government," he added.

Iraqi officials said about 4,000 fighters from the militia group were heading to the northern edge of Ramadi as a first step to eventually rolling back the IS jihadists from city, which fell to the extremists on May 17.

The Iraqi government and its American allies had been reluctant to send in Iran-backed Shiite militia in Anbar — a predominantly Sunni province. But the IS advance in Ramadi — a major blow for both Baghdad and the US-led coalition — prompted Iraq to approve the deployment of the militias.

Washington is wary of the militias with ties to Iran but has said it would support a role for all forces that remain under the authority of the Iraqi government.

"Many of them (militias in the Anbar area) are under the control of the central government," Warren said.

But he added: "I don't know whether if any that are there are not under the control of the government."

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