BAGHDAD - After months of sluggish progress, stalled advances, and outright failures, Iraqi troops and militias backed by U.S.-led airstrikes have surrounded the key city of Ramadi and appear poised to launch a new attempt to wrest it from the Islamic State.

The battle that is shaping up threatens to turn into a drawn-out siege, with thousands of residents caught in the middle as the forces try to wear down the extremists since they took over the city in May. Western officials and analysts warned that the strategy of a methodical, slow siege could make the fight even more difficult.

On Monday, the Iraqi military dropped leaflets into the city, telling the remaining residents - estimated at anywhere from 4,000 to 10,000 - to leave, the strongest signal yet that an assault was imminent.

Residents told the Associated Press on Tuesday that the extremists had clamped down, setting up checkpoints across the city to monitor civilians' movements.

"Loudspeakers from mosques give warnings that civilians are not allowed to leave, and anyone who tries to do so will be either arrested or killed," one resident said, speaking on condition of anonymity for fear for his safety.

For several months, Iraqi troops and an umbrella group of militias have been fighting in Anbar. Although progress was often slow, they clawed back territory surrounding the city. In recent days, their determination to retake Ramadi has been boosted by a victory in northern Iraq by Kurdish forces, who recaptured the town of Sinjar.

The most recent estimates from the U.S.-led coalition say there could be as many as 1,000 Islamic State fighters inside Ramadi. Iraqi officials said their forces surrounding the city number several thousand.

A Western coalition official who has knowledge of the Iraqi forces' level of preparedness said an operation in Ramadi would probably involve high casualties - something the Iraqis "aren't willing to accept" at this point.

"They just aren't there yet," he said.