The explosions, which also wounded at least 50, took place in the Alawi district, close to the ministries of justice, foreign affairs and other government offices.
Iraq's security has come under growing strain as the sectarian conflict in neighbouring Syria reignites Iraq's own combustible Sunni-Shi'ite mix.
Police said two car bombs were detonated, one of them near the justice ministry building, before a suicide car bomber blew himself up near an interior ministry office.
A second suicide car bomber then walked into the justice ministry and militants attacked the building, clashing with Iraqi security forces. Police said the sound of gunshots was still audible.
Among the dead were at least 6 policemen and 12 civilians, police and medics said.