Hundreds of civilians have over the past few days managed to flee the area, which lies west of the Kurdish-controlled city of Kirkuk and about 220 kilometres (140 miles) north of Baghdad.
Hawijah and its surroundings are one of the last major areas east of the Tigris still controlled by IS and possibly the next target of the forces battling the jihadists in Iraq.
"Our forces received 600 people yesterday and offered them assistance," a brigadier general with the Kurdish peshmerga forces told AFP.
"We heard from them that Daesh (IS) is holding hundreds of families hostage and has executed young men for escaping from the land of jihad (holy war) to the land of the infidels," he said.
A police colonel also said that several people had been shot dead by IS fighters as they attempted to flee the area recently.
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A local tribal leader urged Iraqi forces to step up operations aimed at retaking Hawijah and rescue trapped civilians.
"We are facing the risk of a massacre and the government has to move quickly," Sheikh Anwar al-Assi told AFP.
After retaking much of the vast western province of Anbar in recent months, including the IS bastion of Fallujah in June, Iraqi forces are training their sights on remaining jihadists strongholds in the north.
The ultimate target is Mosul, the country's second city and the de facto Iraqi capital of the jihadist organisation's self-proclaimed caliphate.
Kurdish and federal forces have held positions around Hawijah for months, imposing a loose siege on the city but stopping short of launching a fully-fledged assault to retake it.
Assi estimated the number of people still living under IS rule in the Hawijah area at 100,000.