By Phil Stewart

WASHINGTON (Reuters) - The Pentagon on Tuesday said it was "unhelpful" for Iraq's Shi'ite militia to have announced an openly sectarian code name for the operation to retake the Sunni city of Ramadi and added that, in the U.S. view, the full-on offensive had yet to begin.

A spokesman for the Shi'ite militias, known as Hashid Shaabi, said the code name for the new operation would be "Labaik ya Hussein", a slogan in honor of a grandson of the Prophet Mohammed killed in the 7th Century battle that led to the schism between Shi'ite and Sunni Muslims.

The United States has been vocally advocating for Iraq to tread carefully in employing Shi'ite militias to help Iraqi forces retake the city, which fell to the Islamic State a week ago in Baghdad's biggest military setback in nearly a year.

Asked about the openly sectarian codename, Pentagon spokesman Colonel Steve Warren said: "I think it's unhelpful."

Warren said the key to victory would be a unified Iraq "that separates itself from sectarian divides, coalesces around this common threat."

U.S. Defense Secretary Ash Carter said over the weekend that Iraqi forces showed no will to fight against Islamic State militants during the fall of Ramadi a week ago, remarks that drew a rebuke from Iraqi Prime Minister Haidar al-Abadi.

Warren elaborated on those remarks on Tuesday, noting that the Iraqi forces "vastly outnumbered their enemy yet they chose to withdraw." He cited a host of problems that preceded the Iraqi pullout from Ramadi.

"Their morale had slipped, their leadership was not up to par. They believed that they were not receiving the support that they thought they needed," he said.

The regular Iraqi military's failure to hold Ramadi has forced the government to send Iran-backed Shi'ite paramilitaries to help retake the city.

The Shi'ite militiamen, supported by a smaller cadre of government troops, advanced on Tuesday to within a few kilometers of a university on Ramadi's southwestern edge.

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Warren described these as "shaping operations" ahead of a proper offensive.

"Shaping operations in this case are operations in order to secure lines of communication, secure key road junctures and intersections, secure certain terrain ... prior to a full-on offensive" Warren said.

(Reporting by Phillip Stewart; Editing by Doina Chiacu and Andrew Hay)