The car blew up at the gates of the centre, which is housed in Muthenna airport, causing a blast which was heard throughout the city.
Witnesses said a car drove into a crowd of about 100 people who were queuing to volunteer, before exploding.
One witness, US officer Colonel Mike Murray, said the attack was by a suicide bomber.
Iraqi security official Yas Khudair said: 'All of the victims who came here are poor people trying to earn a living. They wanted to volunteer to support their families'.
The same recruitment centre was hit by a car bomb five months ago when up to 47 people died.
UK Foreign Secretary Jack Straw said the attack would not affect the handover. 'We and the Iraqi people will not be deterred. The transfer of power will take place. Iraqis will take control of their lives.'
On the same day, a Hungarian soldier was killed in a suspected roadside bomb that hit a military convoy in southern Baghdad.
Hungarian Defence Minister Ferenc Juhasz praised the soldier and said he had 'died a hero's death'.
The soldier was the first military death for the 300-strong Hungarian battalion, who operate under Polish command.
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