The first blast tore through the Justice Ministry and minutes later the second blast struck the building housing the offices of the Baghdad governor.
Prime Minister Nuri al-Maliki's office said that the bombs were meant to sow chaos in Iraq similar to attacks on 19 August against the finance and foreign ministries, and were aimed at stopping an election in January.
A statement from his office said: 'It is the same black hands who are covered in the blood of the Iraqi people. They want to cause chaos in the nation, hinder the political process and prevent the parliamentary election.'
The area near the provincial building was flooded and fire fighters pulled charred and torn corpses off the streets. Burnt cars piled up nearby. Workers on cranes combed the broken face of the Justice Ministry, pulling out bodies wrapped in blankets.
'I don't know how I'm still alive. The explosion destroyed everything. Nothing is still in its place,' shop owner Hamid Saadi told Reuters by telephone from near the Justice Ministry.
US forces provided forensics teams and bomb experts. Police sources said the bombs were carried in vans driven by suicide bombers while others said a truck and car were used.
The al-Mansour hotel, which houses the Chinese embassy and several foreign media groups, was also damaged.
US officials say the attacks are aimed at reigniting the sectarian conflict that gripped Iraq after the US-led invasion that deposed Saddam, or at undermining confidence in Mr Maliki before the parliamentary poll.
Mr Maliki is widely expected to campaign on improved security.
The attacks were launched as his government tries to sign multi-billion dollar crude deals, expected to turn Iraq into the world's third largest oil producer.
US President Barack Obama said after the attacks that the bombings were 'outrageous' and an attempt to thwart Iraq's progress.
He said: 'These bombings serve no purpose other than the murder of innocent men, women and children, and they only reveal the hateful and destructive agenda of those who would deny the Iraqi people the future that they deserve.'
The White House said that Mr Obama had phoned Iraqi Prime Minister Nuri al-Maliki and President Jalal Talabani after the attacks and pledged that the US would 'stand with the Iraqis'.
