A cafe and bazaar were the apparent locations of the explosions, which were clearly heard throughout downtown Baghdad and which sent thick clouds of smoke into the air.
The explosions occurred in quick succession injuring numerous people. At least two of the dead are US citizens.
While the Green Zone has come under attack before from mortars and rockets, Thursday's bombing is the most serious attack to date.
The nationalities of the victims were not immediately known.
Investigators do not believe the explosions were caused by mortar or rocket attacks or by a car bomb, and are examining the possibility that the bombs were carried into the compound.
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