Police said there were casualties from Thursday's attacks, but it was not yet clear how many.
"We felt a strong blast. I came out and saw a blown up car and some people dead on the street," policeman Haider Abd al-Hussain said.
Another policeman at the scene said one of the bombers used a police car in the attack outside a checkpoint used by journalists, contractors and other civilians working in the compound.
Police sources said the second bomber, strapped with explosives, attacked police who rushed to the scene.
Third man wounded
An Interior Ministry source said police noticed a wounded man also had wires hanging out of his clothing, suggesting a third bomber may have been thwarted.
Other reports said a third bomber was killed by police.
Fighters, bent on toppling the fledgling Iraqi government, frequently attack checkpoints outside the Green Zone and fire mortars at the area.
The blasts came on a new public holiday, announced last month and marking the 1958 revolution that overthrew the British-installed monarchy.
The explosions were followed by a mortar attack, police said.
Journalists in central Baghdad,too, heard heavy machine-gun fire from the same area after the blasts.