As ground forces push west across Iraq in the fight against the Islamic State group, civilians are increasingly caught in the crossfire.

Iraq's elite counterterrorism forces say an estimated 20,000 civilians are trapped in the small western town of Hit, where Iraqi forces have recently relaunched an offensive aimed at cutting critical IS supply lines to neighboring Syria. The civilians, Iraqi commanders and U.S.-led coalition officials say, are slowing operations, making it more difficult to use airstrikes to clear terrain ahead of ground troops.

A single white flag flies above Mursid Nigris's house on the edge of a palm grove on the western outskirts of Hit, which lies in Anbar province, 85 miles (140 kilometers) west of the Iraqi capital. Behind his home, black clouds of smoke rise from the town's center. Counterterrorism forces pushed IS out of this largely agricultural neighborhood on the outskirts of Hit Thursday, but have made little progress since.

Iraqi forces relaunched the operation to take Hit early Thursday morning under cover of coalition airstrikes. The town lies along a supply line linking the extremist group's fighters in Iraq to those in neighboring Syria. Iraqi commanders say retaking the town will be a key step to link up government forces in Iraq's west and north in preparation for an eventual push on Mosul.

The original push was delayed by political instability in the capital, Baghdad. When anti-government protests escalated last month, Iraqi Prime Minister Haider al-Abadi pulled some military units from Anbar to Baghdad.

After parts of Ramadi fell to Iraqi forces in December last year, the government and the U.S.-led coalition have tried to build on those gains, moving up the Euphrates river valley and clearing IS from villages as they went. In the months that followed, thousands of civilians fleeing Iraqi military operations across Anbar descended on Hit.

While Iraqi forces have evacuated thousands of families as they've retaken territory from IS, thousands more simply fled or were forcibly moved by IS fighters as they retreated. The operations to Hit's north, west and south have effectively boxed civilians in to the small town.

"They honestly are just looking for a safe place they can reach quickly, they don't care if it is IS controlled or not," said a captain with the counterterrorism forces overseeing the Hit operation.

He spoke on condition of anonymity as he was not authorized to brief the press.

Nigris, a 45-year-old farmer, is hosting 20 members of his extended family in his simple farm house. Although Hit fell to IS last summer, the town has remained relatively safe as airstrikes and the initial clashes between IS and Iraqi forces focused on the larger cities of Ramadi and Fallujah.

"Daesh would come to our house and interrogate us," Nigris said, using an arabic acronym for IS. "They would demand we confess we are with the police or the military."

Eventually, however, fighters largely left his family alone. The problem then was the longer IS stayed in Hit, the harder it became to find food, water and fuel for his family, Nigris said. Trade with the rest of the country ceased, and damage to the town's infrastructure meant few people had access to running water.

"Militarily we could liberate Hit in just one day," said Gen. Abdul-Ghani al-Asadi, the top counterterrorism forces commander, "but we are having problems with the families stuck inside."

Al-Asadi said the civilians have prevented the coalition from launching airstrikes and Iraqi military units from using heavy artillery. While the counterterrorism forces are some of Iraq's most capable ground forces, they are still heavily reliant on airstrikes to retake ground.

"This is a bigger problem than we saw in Ramadi. That city didn't contain that large of a number of civilians, at least not in such a concentrated area," al-Asadi said.

When Iraqi forces closed in on Ramadi in December, IS blocked the main roads out of the city, trapping families inside. Later, as the fighters were pushed out of some neighborhoods, they forced civilians to flee with them.

Hit is roughly a fifth of the size of Ramadi. Initial estimates of the number of civilians in Ramadi were around a thousand, but as Iraqi forces cleared the city many thousands more were discovered.

Al-Asadi said his forces are prepared to help evacuate civilians in Hit as they did in Ramadi, where special forces evacuated families as they took over territory. He added, however, that he believed the large number of trapped civilians would become an ever bigger complication facing operations as forces move north to the IS-held city of Mosul.

The captain with the counterterrorism forces overseeing the Hit operation says he doesn't believe IS has the manpower in Hit necessary to move civilians with them as they flee, but his men are still struggling to avoid civilian casualties when coordinating airstrikes.

"We're telling the civilians to mark their houses in a certain way so we can tell who is and who isn't a fighter," the captain said.

Initially he said his forces asked civilians in Ramadi to carry white flags as they fled, but the symbol was quickly adopted by IS to disguise counterattacks.

"It's not easy always coming up with new signs," the captain said, "the last time I saw a white flag it turned out to be a VBIED," he said using an American military acronym for a car bomb.

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Associated Press writer Khalid Mohammed in Hit, Iraq contributed to this story