According to a security official, just before Friday midnight a car rigged with explosives was detonated at the car park of al-Nakheel Mall in Palestine Street in eastern Baghdad.
An assailant blew up his explosive-laden car at the busy street outside the mall building shortly afterwards.
The explosions set ablaze a number of cars parked at the parking lot and outside the mall, and damaged many others.
An unnamed source at Baghdad Health Directorate told Arabic-language al-Forat news agency that 35 people have been killed and 40 others injured in both acts of terror.
No individual or group has claimed responsibility for the assaults yet, but such incidents are usually blamed on the Takfiri Daesh (ISIS) terrorist group.
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