"The dead include three Department of Defence civilians," Lieutenant-Colonel James Hutton said. Six Iraqis were also killed.
He said the wounded included 13 Iraqis, three US citizens and two US soldiers.
A revised figure later put the number of US contractors killed at four. US officials said the four were employees of the private security firm DynCorp.
After the blasts, thick black smoke billowed from the heavily fortified zone, which houses Iraqi interim government offices and the US and British embassies, witnesses said.
The exact location of the blasts was not known, but smoke appeared to be rising from near the main entrance to the Green Zone.
Fighters have frequently attacked the sprawling compound on the western bank of the Tigris river in their campaign against US forces and Iraq's interim government.
Meanwhile, 15 members of the US-established Iraqi national guard were killed in an attack on a building housing Iraqi police and guardsmen in al-Qaim city near the Iraqi-Syrian border.
Aljazeera said many employees had refused to go to work in the border town, while others evacuated the building just minutes before the attack.
Officials expect anti-US fighting
to last for many more months
Elsewhere, unknown assailants in a car killed two senior Iraqi army officers in Baquba, north of Baghdad, one of their colleagues said.
He identified the officers as Brigadier-General Nadim Muhsin and Lieutenant-Colonel Imad Awad.
There was no immediate word on the motive for the killings. But anti-US fighters frequently attack members of Iraq's security forces, accusing them of collaboration.
About two hours before the attacks in the capital, a roadside bomb killed a civilian and wounded six Iraqi national guardsmen in the northern city of Mosul, while a car bomb exploded near a US military convoy, Iraqi police and hospital sources said.
They said the roadside bomb exploded in the city's northern Baladiyat district. The driver of a passing construction vehicle was killed. The six guardsmen sustained light wounds.
The car bomb detonated as five US Stryker fighting vehicles were passing through the Islah district in western Mosul, witnesses said. There was no immediate word on casualties from that blast.
Also on Thursday, two US soldiers were killed, one in an attack in central Baghdad and another by a homemade bomb on the eastern side of the capital, which also wounded two, a US military statement said.
There have been 1086 US soldiers killed in Iraq since the US-led invasion in March 2003, according to the latest Pentagon figures.