The al-Qaida-linked group claimed it carried out a first attack on 5 July and another the following day in al-Khalis, north of Baghdad, which killed two relatives of a local official, "including the brother of the official, known for his hatred and hostility towards the mujahidin."
"On 6 July, when the infidels and agents gathered for a so-called memorial service, the group successfully drove a car bomb at the site where it exploded," added the statement on Sunday.
Titled Statement on the Liquidation of a Group of Spies and Agents, and signed by its "military wing", the group warned that other "infidels" would "experience the same fate if they don't repent".
The 6 July attack, the bloodiest car bombing since the handover of power by the United States on 28 June to a caretaker government, killed at least nine people and wounded 37.
The provincial governor along with many members of the local council were at the memorial service for a local official killed in an attack two days earlier along with a friend.
Uday Adnan Khadran, a Shia Muslim and administrative chief of Khales, was wounded and lost two brothers in the bombing, police said.