KIRKUK, Iraq (Reuters) - Hundreds of displaced Sunni Arab families have had to leave Kirkuk after an Islamic State attack on the Kurdish-controlled city which authorities suspect was helped by Sunni sleeper cells, humanitarian workers and residents said on Tuesday.

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The Sunni families, who had been sheltering in Kurdish-controlled Kirkuk province from the conflict with Islamic State, began moving out after authorities told them on Sunday to leave or face being forcibly expelled, the sources said.

About 330,000 Sunni Arabs have taken refuge in the oil-rich Kirkuk province in the last two years, after Islamic State swept through northern, central and western Iraq in 2014.

Some had fled because of the fighting and others because of the hardline Sunni group’s harsh rules and the difficult living conditions in their villages and towns.

Islamic State fighters stormed police stations and buildings in Kirkuk on Friday, killing about 100 security force members and civilians. Sixty-three militants also died in the heavy fighting that lasted until Sunday, when authorities restored control.

The jihadists carried out the operation to relieve pressure on Mosul, the last major city stronghold of Islamic State in Iraq, where the group is fighting off an offensive by Iraqi army units and Kurdish forces backed by a U.S.-led coalition.

The militants are suspected to have come from Hawija, a pocket still under their control west of Kirkuk, but authorities also suspect that they were assisted by sleeper cells hiding among the displaced people or even by Sunni Arab residents.

More than 250 families were counted leaving at a main exit checkpoint on Monday and more were crossing on Tuesday, a local humanitarian worker said, adding that some were heading to other camps for displaced people and others trying to return home.

Spokespeople at the migration ministry in Baghdad and the Kurdish provincial authorities declined to comment.

Kirkuk is the most disputed area of Iraq because of its complex population mix. The Kurds took full control of the province in 2014 after Islamic State overran much of the north of the country and several divisions of the Iraqi army disintegrated.

Arabs complain that Kurds have since flooded to Kirkuk to tilt the demographic balance, while Kurds say they are simply redressing historic wrongs perpetrated by Saddam Hussein, the Sunni Arab leader toppled by the United States in 2003.

Saddam’s policy of “Arabisation” in the north during his quarter century in power led to many Kurdish villages being razed and hundreds of thousands of people being displaced to ensure Arab dominance over local Kurds, Turkmen and Assyrian Christians.