The group said in a statement posted online late Saturday that two of the attacks were carried out by suicide bombers - Abu al-Qaaqaa al-Almani and Abu Abdul-Rahman al-Shami. The names indicate they were German and Syrian respectively.
The jihadi group said the other two attacks were parked car bombs. It said the bombings targeted Iraqi security forces as well as Shiite volunteers who have taken up arms following the Sunni militant blitz in recent weeks.
The authenticity of the statement could not be independently verified, but it was posted on a militant website frequently used by the group.