(CNN) Iraqi troops have retaken the city of Ramadi from ISIS, the country's military said.

Troops have raised the Iraqi flag on top of the government compound in central Ramadi, military spokesman Brig. Gen. Yahya Rasoul said Monday.

Ramadi, in Anbar province, about 110 kilometers (70 miles) from Baghdad, fell to ISIS in May , a major setback in the country's effort to contain the terror group.

Iraqi TV showed Iraqi soldiers celebrating what the government is calling the "liberation" of the city. During the live coverage, explosions and gunfire could be heard in the background. Ramadi is a predominantly Sunni Arab city, and the Iraqi military forces are mostly Shiites.

'A significant accomplishment'

The U.S.-led coalition that has been launching airstrikes on ISIS targets addressed the positive development Monday.

"The clearance of the government center is a significant accomplishment and is the result of many months of hard work by the Iraqi Army, the Counter Terrorism Service, the Iraqi Air Force, local and federal police and tribal fighters," coalition spokesman Col. Steve Warren said.

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Warren told CNN that Iraqi forces have made "great progress" securing what is essentially the city hall of Ramadi and areas south to railroad tracks, and have cleared some major neighborhoods. But there remain pockets of insurgents -- some six to eight men -- fighting back in some neighborhoods, he said.

ISIS is well known for planning homemade bombs to ambush enemies. "There's a real threat of unexploded ordinances and booby-trapped houses," Warren said.

CNN's Becky Anderson, reporting from the United Arab Emirates capital of Abu Dhabi, noted the coalition spokesman used careful wording in the statement that pointed out the city government center had been retaken.

"Reports suggest that it is likely that ISIS has moved from the government compound to the north of the city, and there's every chance they could regroup," Anderson said.

It's possible that the Iraqi military's achievement is a symbolic victory, she said, and what happens next is critical.

The city in central Iraq has strategic importance, with roads into Jordan and Syria, and Anbar province is the heartland of Iraq's Sunni Muslim population.

CNN contributor Michael Weiss , author of "ISIS: Inside the Army of Terror," said a wait-and-see approach to what's happening in Ramadi is necessary.

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Noting the Shiite-majority Iraqi military, he said the Sunni population in Ramadi might perceive the troops as worse than ISIS. "The real test is can they (the Iraqi forces) hold onto" the city, he said.

Warren said that it doesn't appear that ISIS has the strength to take Ramadi back.

Kimberly Dozier, a CNN contributor and journalist who has reported extensively from Iraq, pointed out that the Iraqi military has previously overstated military successes and that's a reason for pause. Earlier this year the Iraqi army retook the city of Tikrit from ISIS but it took months, Dozier said, for the Iraqis to get the electricity back on for the population and to make it safe and practical for residents to return.

"Ramadi will be a new test," she said. "This will be a test of (the Iraqis') capability to keep the peace and inspire confidence."

'We will liberate' other cities

Rasoul said he is confident the military will retake other cities captured by ISIS.

"We will liberate all the other places like we liberated Jurf al-Nasr and Tikrit and Baiji and other areas," he said.

Fighting in and around the city is likely to continue for some time , analysts say. ISIS is expected to stage ambushes in outlying suburbs to prevent the city's pacification and rehabilitation.

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In the view of the Institute for the Study of War, "Ramadi will remain exposed to counterattacks by ISIS, particularly from the north from ISIS-held Hit district, if (Iraqi security forces) shift forces away from Ramadi to focus on other operations."

The public is broadly unhappy with the nation's progress, with nearly three-quarters of Americans saying they are not satisfied with how the war on terror is proceeding. That figure, following terrorist attacks this fall in Paris and San Bernardino, California , is well above the previous high of 61% who said they were dissatisfied in August 2007.

More than a year after U.S. airstrikes against ISIS began, Americans are no more likely now than they were last fall to consider the conflict with ISIS a war. Fifty-seven percent of those polled say the U.S. is involved in a military conflict rather than a war, while 40% call it a war.

In late September 2014, the numbers were almost exactly the same: 40% labeled it a war, 59% a military conflict.