HIT, Iraq — As they advanced on the Islamic State-held town of Hit, Iraqi counterterrorism troops had to decide how to press the attack. If they stormed in with armor and airstrikes, they risked heavy casualties and might allow the militants to flee.

Gen. Abdel Ghani al-Asadi, the commander of the elite troops, chose a different approach: Surround the strategic western town with a slow and methodical cordon, trapping the extremists inside.

It’s a tactic that’s been used elsewhere to claw back Iraqi territory that was seized by the Islamic State group in 2014.

While the decision may have been more time-consuming, allowing the militants in Hit to dig in, lay defenses and launch attacks that initially also trapped tens of thousands of civilians, Iraqi forces believe the approach is a key to making their territorial gains stick and reduce their casualties.

Six counterterrorism battalions pushed up from the west last weekend to cut off Hit’s northern edge, zigzagging in the soft desert terrain and taking more than 12 hours to advance only a few miles.

“We don’t want them to be able to flee,” al-Asadi said. “We want them to stay inside so we can finish them.”

If the militants escaped, he said, they would probably return and infiltrate the town once his men had moved on to the next battle.

Hit, in Anbar province west of the capital of Baghdad, sits along an ISIS supply line that links Iraqi territory controlled by the extremist group with its base in Syria. Officials in the Iraqi military and the U.S.-led coalition believe that by clearing the town, they can build on recent territorial gains in the vast province.

That would move them closer to two major goals: isolating the Islamic State-held city of Fallujah, 40 miles west of Baghdad, and linking up government forces in the west and the north in preparation for an eventual push on Mosul, Iraq’s second-largest city that also is held by the extremist group.

As Iraqi forces closed in on Hit, al-Asadi said he ordered the town’s main bridge over the Euphrates River destroyed by a coalition airstrike to slow the flight of fighters. In the days that followed, dozens of boats were also destroyed by coalition bombs, the Pentagon said.

In the initial stage of the operation last month, some militants sought to knit themselves further into the civilian fabric of the town. Fighters vanished from Hit’s main streets, occupying abandoned houses or forcing their way into homes where civilians were living, according to residents who evacuated.

“They began moving more and more into the narrow side streets and the civilian areas,” one resident said, speaking on condition of anonymity in order to protect the safety of relatives still trapped in Hit.

Al-Asadi said his men were increasingly finding fighters from the Islamic State group posing as civilian refugees.

“One of the ways we can tell is you can see they shaved their beards very quickly,” al-Asadi said, smiling. “They have cuts from the razor on their faces.”

Because tens of thousands of civilians were still inside Hit when the operation began, only about 20 coalition airstrikes per week were launched to clear territory, Iraqi commanders said.

By contrast, coalition jets conducted 20 airstrikes in a single day when Iraqi forces retook the northern town of Sinjar last year – and more than 60 in the week it fell. But Sinjar was smaller than Hit, and almost all civilians had left.

The trickle of civilians from Hit turned into a flood Monday as a column of Humvees carrying elite Iraqi forces began rolling through agricultural neighborhoods and residential blocks. Thousands of civilians filled Hit’s northern main road, the only route open.

While civilians were being loaded into trucks to be taken to a camp, a bomb exploded with a plume of orange smoke along the path they had just traversed. Commanders said it had been triggered prematurely and no one was hurt.