The attacks, which wounded dozens more, come as security forces battle militants in the western Anbar province, including the Islamic State of Iraq and the Levant (ISIL), a powerful jihadist group that has exploited the chaos in neighbouring Syria.
With violence at its highest level since 2008, diplomats have urged the Shiite-led government to reach out to Sunnis in order to undercut support for militancy, but Prime Minister Nuri al-Maliki has taken a hard line ahead of April's parliamentary elections.
Among the attacks was a car bomb just opposite the foreign ministry on the edge of the heavily-fortified Green Zone, home to parliament and the US embassy.
A suicide bomber hit a restaurant, while a vehicle rigged with explosives was detonated in a market for car spare parts.
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The toll could have been higher still, but security forces managed to defuse a roadside bomb near the oil ministry in central Baghdad.
The area surrounding the foreign ministry in central Baghdad has been hit by explosions in the past, notably in August 2009, when a massive truck bomb devastated the building, and again ahead of an Arab summit in the Iraqi capital in 2012.
More than 1,000 people were killed in January of this year, according to government data, as security forces have struggled to curb bombings while also battling jihadists and other militants who have seized territory in the western Anbar province.