"Our forces have arrested seven members of an Al-Qaeda cell who confessed to kidnapping a seven-year-old girl in Yarmouk (western Baghdad neighbourhood) because her father, a teacher, had refused to pay ransom for her," Qassim Atta said.
In video confessions of two of the suspects shown to journalists, they both claimed to have killed dozens of police officers using silenced guns.
On statements posted on the Honein Islamist forum, Al-Qaeda has claimed responsibility for more than 60 attacks in Iraq over the past two months, primarily targeting the military.
It has also said that 12 prisoners who escaped from prison in January in the southern city of Basra had been killed last month in a suicide attack on a police station in the southern city.
Al-Qaeda's front group in Iraq also said it carried out last month's double car bombing outside the governor's home in the central city of Diwaniyah in which 26 people were killed, but the official escaped unharmed.
Atta cautioned people to "move away from the scene of an attack" because insurgents often explode a second bomb after people gather in an order to ramp up the number of casualties.