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.