A senior officer from the counter-terrorism forces which led the recapture of nearby Ramadi three months ago said Thursday his troops are one kilometer from the town center, 130 km (80 miles) west of the capital Baghdad.
The operation began at 0600 (0300 GMT) and was progressing swiftly, another officer was quoted as saying.
Hit is strategically located on the Euphrates River near the Ain al-Asad air base and its recapture would push Daesh further west towards the Syrian border.
The liberation of the town would also cut a connection to the northern town of Samarra and leave Fallujah as the only stronghold left for ISIS near the capital.
The Iraqi army and volunteer forces have made remarkable achievements in pushing back the Takfiri militants in recent months and have pledged to retake the northern city of Mosul later this year.
In a statement announcing the advance in Hit, the military said the offensive was backed by airstrikes from the Iraqi army and air force.
The statement called on civilians in Hit, thought to number in the tens of thousands, to move away from Daesh positions, saying those targets will be destroyed.
The Takfiri terrorists have regularly used civilians as human shields, a tactic aimed at slowing the advance of Iraqi forces and complicating airstrikes essential to the ground advance, Press TV reported.
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