The three car bombs and one roadside bomb, which hit three separate areas of Baghdad, also wounded at least 40 people, the officials said.
The bombings come as militants hold the city of Fallujah, just 60 kilometres from Baghdad, as well as parts of Ramadi, farther west.
Anbar has in recent days seen the worst violence to hit the province in years, killing over 160 people on Friday and Saturday alone.