BAGHDAD — Six members of an Awakening Council, groups composed mostly of Sunni Muslims who have turned against the insurgency, were killed early Thursday after they mistakenly fired on U.S. soldiers in the north, the Iraqi police said.

The U.S. forces returned fire, killing them and two women in nearby houses, the police said. A police commander said the group had thought the Americans were insurgents.

Local U.S. commanders said they could not confirm the incident. But it appeared to underscore the growing danger to Awakening Council members, wedged between U.S. forces and the insurgent groups many of them once supported, amid a recently begun operation to go after insurgents more aggressively in certain areas.

In recent weeks, Sunni extremists have increasingly aimed their attacks at Awakening Council members, killing at least 33 people in car bombings aimed at the groups this week alone. The U.S. military reported Thursday that they had killed 7 insurgents and arrested 16 in north and central Iraq.

The firefight between U.S. troops and Awakening Council members occurred near the village of Al Raween in Salahuddin province, northeast of Baghdad, an area that has remained restive despite a 60 percent decrease in violence in Iraq since last summer, after the U.S. military increased its troop strength by 30,000 soldiers.

Also on Thursday, nine members of the same family — a couple and their seven children — were found dead, apparently executed, in their house in Auja, 70 miles south of the firefight with Awakening Council members, in the same province. Auja is the birthplace of Saddam Hussein. The children ranged in age from 7 to 17 years.

Ragi Ali, 25, the brother of the slain father, Labeeb Ali Khatir, 50, said each family member had been shot with one bullet in the head and another in the stomach. He said a note was left, signed in red by Tawhid Wal Jihad, a group that is part of the Sunni insurgency. The family is distantly related to Saddam and lives next to the cemetery where he was buried after he was executed in December 2006.