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Iraqi forces entered the town of Hit on Monday, a week after launching an operation to retake the strategic Anbar town from Islamic State (IS) militants, commanders at the scene said.

Iraq's elite counterterrorism forces, who are leading the offensive, said they are clearing IS fighters from Hit's northern neighborhoods as they push in toward the town center.

Iraqi and coalition officials say Hit - which lies along the Euphrates river valley in Iraq's vast Anbar province - is strategically important as it sits along an IS supply line that links the extremist militants in Iraq to those in Syria.

Iraqi forces escorted thousands of civilians fleeing the fighting as government troops advanced under cover of heavy airstrikes and artillery fire.

Families, many with small children and elderly relatives, said they had walked for hours through desert littered with roadside bombs to escape the violence.

Azha Hadel and her three young children walked for five hours from her neighborhood in northern Hit to the city's outskirts, where they were loaded into open trucks by Iraqi security forces.

"Honestly we have no idea where we are going," Hadel said, her and her children's faces sunburned from the long day outdoors.

Iraq's counterterrorism forces estimate more than 20,000 civilians remain trapped inside Hit.

"We want to go anywhere, anywhere that's safe." Iraqi counterterrorism forces at the scene said the families were being brought to a nearby camp.

Behind Hadel, black smoke rose from Hit as buildings and vehicles hit by airstrikes burned.

Hundreds more civilians were slowly walking out of the town by the evening.

Iraqi troops, who had spent hours clearing the territory before their assault, instructed families not to stray from the tire marks to avoid explosives. Piles of rocks and scrap metal marked unexploded bombs along the path.

Iraq's counterterrorism forces estimate more than 20,000 civilians remain trapped inside Hit. The large number of people in such a small area is making it difficult to quickly clear territory with airstrikes, according Gen. Abdul Ghani al-Asadi, the head of Iraq's counterterrorism forces.

On Sunday, the US-led coalition launched three airstrikes that targeted IS fighters, a car bomb and a heavy machine gun, the Pentagon said in a statement.

The Hit offensive comes after a string of territorial victories for Iraqi forces over the past six months.

Most recently Ramadi, the capital of Anbar province, was declared fully "liberated" by Iraqi and coalition officials in February.

Coalition officials estimate IS has lost more than 40 percent of the territory it held in Iraq after the summer of 2014.

"Daesh fighters now are stuck," said captain Aysar Hassan, who is with a counterterrorism battalion leading the fight, using an Arabic acronym for IS.

He had expected heavier resistance as his men approached the city center but that was not the case.

"In Ramadi they all had places to run away to, now they don't have a way to escape," Hassan said.