The violence, which left dozens more wounded, was the worst since a series of explosions across the Iraqi capital on December 22 killed 60 people, shortly after the crisis erupted and following the withdrawal of US troops from the country barely two weeks ago.
In the north Baghdad neighbourhood of Kadhimiyah, twin car bombs exploded at around 9:00 am (0600 GMT), at intersections near to each other, officials from the interior and defence ministries said.
The blasts killed 12 people and wounded 22 others, the defence official said, while the interior ministry source put the toll at 15 dead and 31 wounded. Both spoke on condition of anonymity.
And in Sadr City, another Shiite district in the north of the capital, a booby-trapped motorcycle exploded at around 7:00 am (0400 GMT) near a group of day labourers waiting to pick up work, killing seven and wounding 20 others, the interior ministry official said.
A short time later, twin roadside bombs detonated near the district's main hospital as victims were being ferried in, killing two more people and wounding 15, the official said.
The defence ministry official also put the combined toll from the Sadr City attacks at nine dead and 35 wounded.
The United States and United Nations have urged calm amid the political standoff and called for national leaders to hold talks to end the row, but no such meetings have yet taken place.
Prime Minister Nuri al-Maliki on Wednesday backed off threats to fire ministers from the Sunni-backed Iraqiya bloc who have boycotted cabinet, the latest in an apparent toning down of the crisis.
The standoff was sparked by the authorities' decision to issue an arrest warrant for Vice President Tareq al-Hashemi on terror charges.
Hashemi, who is holed up in the northern autonomous Kurdish region, denies the charges and his Iraqiya party has boycotted cabinet and stayed away when parliament re-opened on Tuesday.
Sunni Deputy Prime Minister Saleh al-Mutlak, also a member of Iraqiya, has decried Maliki as a dictator "worse than Saddam Hussein", and the premier has called for him to be sacked. MPs were due to have considered that request on Tuesday, but the motion was not discussed or voted on.
Violence is down nationwide since its peak in 2006 and 2007, but attacks remain common, especially in Baghdad. A total of 155 people were killed as a result of violence in December, according to official figures.