Two Sahwa, or Awakening Council, fighters were initially killed when their car was struck by a roadside bomb at around 9:30 am (0630 GMT) in the Al-Nibaie area, north of the town of Mashaada, 30 kilometres (18 miles) from the capital, police First Lieutenant Uday Sarhan said.
When two other Sahwa fighters rushed to the scene of the blast, their vehicle was hit by another roadside bomb, killing both of the car's passengers and two nearby civilians, Sarhan said. He added that there had been no wounded from the two explosions.
A doctor at a hospital in the nearby town of Balad confirmed that four Sahwa fighters and two civilians had died. Al-Nibaie is a desert area that was a stronghold of Al-Qaeda at the height of Iraq's Sunni insurgency in 2006 and 2007.
The tide of that insurgency began to turn partly due to Sunni tribesmen siding with the US military against Al-Qaeda from late 2006, forming the Sahwa, who are called the "Sons of Iraq" by US forces.
Violence is down across Iraq from the peak of the insurgency and sectarian war, but attacks are still common. A total of 185 Iraqis were killed in violence in September, according to official figures.