BAGHDAD - The advance of Iraqi forces into the heart of Ramadi, a restive city that fell to the Islamic State earlier this year, in some ways vindicated the U.S.-led coalition's strategy for rolling back the extremists - but victory has come at a high cost, and the same tactics might not work elsewhere.

The battle for Ramadi was waged by the Iraqi military - rather than Shiite or Kurdish militias - with elite counterterrorism units advancing under the cover of coalition airstrikes and raising the Iraqi national flag over the main government complex in the provincial capital on Monday.

Pockets of resistance remain, but the majority of Ramadi is under government control for the first time since May, when IS militants punched their way into the city with a series of massive suicide car bombs, scattering and humiliating Iraq's beleaguered security forces.

Brig. Gen. Ahmed al-Belawi said "heavy and concentrated airstrikes" by the U.S.-led coalition killed IS fighters, destroyed their vehicles and blew up suicide car bombs before they could be deployed, allowing his forces to advance into the city.

"I think this fight shows the Iraqis are ready to fight and these calls for U.S. ground troops are not the best strategy moving forward," said Ahmed Ali, a senior fellow at the Institute of Regional and International Studies at the American University of Iraq.

"What we saw in terms of the combination of airstrikes and intelligence support and then forces on the ground, it has worked very, very well," he said.

Over the last six months, the coalition has launched more than 600 airstrikes, hitting about 2,500 different targets, U.S. Army Col. Steve Warren, the Baghdad-based spokesman for the coalition, told reporters on Tuesday. He said at its peak there were up to 1,000 IS fighters in Ramadi, and that only 150-250 remain.

But while the airstrikes eventually helped flush out the militants, they smashed large parts of the city into rubble.

Iraqi Prime Minister Haider al-Abadi, who toured parts of Ramadi on Tuesday, had earlier hailed the advance, vowing that 2016 would be "the year of the final victory," when IS would be driven from Iraq.