Islamic State fighters have captured the northern Iraqi town of Zumar and a nearby oilfield after a battle with Kurdish forces who had control of the area, witnesses say.

Islamic State, which staged a lightning advance through northern Iraq in June, has warned residents of nearby villages along the border with Syria to leave their homes, suggesting they were planning an assault, the witnesses said on Sunday.

The group also siezed control of Wana, a town near Mosul Dam in nothern Iraq on Sunday, witnessed and a Kurdish official told Reuters news agency.

The armed group formerly known as the Islamic State of Iraq and the Levant, or ISIL, controls a large expanse of northern and western Iraq, and has threatened to march on Baghdad but has stalled its campaign just north of the town of Samarra, 100km north of Baghdad.

But it has been trying to consolidate its gains, setting its sights on strategic towns near oilfields, as well as the border with Syria so that its fighters can move easily back and forth and bring in supplies.

An official in the Northern Oil Company said Islamic State fighters had taken control of the Ain Zalah oil field and a nearby refinery. The rebels had already seized four oil fields, which help fund their operations.

In a statement on its website, Islamic State said its fighters killed scores of Kurdish fighters in a 24-hour battle and then took over Zumar and 12 villages.

"Hundreds fled leaving vehicles and a huge number of weapons and munitions and the brothers control many areas," Islamic State said, including Zumar and "the area of Ain Zalah which is rich with oil.

"The fighters arrived in the border triangle between Iraq, Syria and Turkey," it said.