Jabbar Yawar, secretary general of the Kurdish peshmerga fighters, said his forces controlled Zumar and reinforcements were on the way.
But four residents in different parts of the town said by telephone that Islamic State fighters were in control.
“Many Islamic State vehicles are wandering the town of Zumar and I can also see the flags on top of buildings,” said one resident.
The group formerly known as the Islamic State of Iraq and the Levant staged a lighting advance through northern Iraq in June, seizing large swathes of land in the biggest challenge to the government of Prime Minister Nuri al-Maliki.
Control of Zumar by Islamic State fighters would give them access to the small Ain Zalah oil field and a nearby refinery. The insurgents have already seized four oil fields, which help fund their operations.
A Kurdish police official in Zumar said Islamic State fighters in pickup trucks mounted with weapons attacked the town from three directions early on Saturday. There were no immediate details of casualties.
Islamic State’s offensive has whipped up sectarian tensions and threatened to dismember Iraq. The sectarian conflict poses the gravest danger to the OPEC member’s stability since the 2003 fall of Saddam Hussein after a U.S.-led invasion.
Shi’ite militias and Kurdish fighters now rival the U.S.-trained and funded Iraqi army in their ability to challenge the insurgents.
Islamic State has declared a medieval-style caliphate spanning parts of Iraq and Syria under its control, alarming other Arab states who fear their advance will embolden militants on their patch.
The Sunni insurgents have stalled their advance towards Baghdad just before the town of Samarra, 100 km (62 miles) north of the capital.-Reuters