Crowds of young male volunteers were gathered at the base when the bombers detonated explosive belts.
Sunni Arab insurgents frequently attack recruiting centres for the US-backed Iraqi government's security forces.
Earlier, an explosion in eastern Baghdad killed four civilians and left 10 others injured.
Police said a bomb had apparently targeted, but missed, one of their patrols. A second bomb detonated at the same time caused no injuries, they added.
Reuters news agency reports that mortar rounds were fired at the police recruiting centre shortly after the bombers struck.
Police also reported that five bodies - all blindfolded and with their legs bound - had been recovered at different locations in eastern Baghdad early on Sunday.
All had been mutilated by torture, they added.
Sunday's attacks took place as the authorities searched for gunmen who ambushed a minibus convoy in the town of Yusufiya, south of Baghdad, a day earlier.
At least 12 passengers were killed in the attack, and about 50 abducted.
It apparently took place when the vehicles were stopped at a false checkpoint.
Yusufiya is a Sunni Muslim stronghold which has become notorious for attacks on Shia Muslims and on American troops.Last Mod: 20 Eylül 2018, 18:16