A month ago the two top U.S. military officials told senators that retaking the western Iraqi city of Ramadi had been elevated to one of three critical objectives leading to the ultimate defeat of the Islamic State’s terrorist army.

Now that major objective is days away.

The Pentagon says “all the pieces are in place” for the Iraqi army and militias, helped by coalition airstrikes, to retake the capital of Anbar province in the heart of Sunni Arab Iraq. The invasion, possibly this weekend, would come five months after an embarrassing retreat in the face of a lightly armed Islamic State invading force.

The Iraqi government has virtually shut off in-and-out routes around the city. Government forces also have captured some neighborhoods on the city’s edge, creating a gateway for advancing troops.

This time U.S. military advisers have built up new Iraqi army brigades almost from the ground up, and believe the 10,000-man force is ready to liberate the city and stand its ground, outnumbering the enemy by a significant margin.

“They have been on the verge of retaking Ramadi for the past four, five months,” said Kenneth Pollack, a military analyst at The Brookings Institution. “They simply have to decide to do it, and take some casualties doing it. But their force outnumbers [the Islamic State] there by 10-to-1 or more. There is certainly some prospect that we finally lit a fire under them to do it.”

It will be an assault eagerly awaited by the Shiite-dominated Baghdad government, the Pentagon and members of Congress who have pressed the top brass to produce a big win against the Islamic State, also known as ISIL and ISIS.

Defense Secretary Ashton Carter and Marine Corps Gen. Joseph Dunford last month told the Senate Armed Services Committee that the Iraqi city is such an important objective it is one of Mr. Carter’s “Three Rs” war strategy: retake Ramadi, drive Islamic state out of its self-proclaimed Syrian capital of Raqqa and conduct air and ground raids.

The Ramadi stalemate has stood in sharp contrast to what happened earlier this month in northern Iraq, where Kurdish peshmerga troops once again showed their willingness to defend their Iraqi homeland. They invaded and recaptured the city of Sinjar with the help of a shape-the-battlefield air bombardment.

It is the same old story. The regular Iraqi army, being pieced back together by American military trainers and advisers, lacked the fortitude to take on Sunni extremists who had routed them from Ramadi 10 months ago. And the Baghdad government has still not armed Sunni tribesman in sufficient numbers to take back Anbar province.

Gen. Dunford, chairman of the Joint Chiefs, said two Iraqi brigades molded by American troops and poised to enter Ramadi are “at a much higher level than the other units.”

Mr. Carter said ousting Islamic State fighters will “build momentum” to “eventually go northward to Mosul,” Iraq’s second-largest city.

The Islamic State typically defends captured urban areas with bands of improvised explosive devices, some placed in vehicles and driven at its attackers.

Army Col. Steven Warren, the top U.S. military spokesman in Baghdad, said Islamic State occupiers are still putting up a good fight as troops move closer.

“The northern access has met with some very stiff resistance, frankly,” Col. Warren said. “The enemy has put up a good fight here in the last couple of days, so they’re continuing.”

He said the Iraqis were able to move about 200 yards on one advance. “So this is slow and incremental work, but they’re continuing.”

Allied jets are hitting targets around Ramadi each day, including fighter emplacements, a tunnel, a building and a bridge. Taking out the bridge made it more difficult for the Islamic State to drive bomb-laden vehicles at Iraqi troops.

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