The attacks, which were apparently coordinated, targeted the Iraqi headquarters of the International Committee of the Red Cross (ICRC) and four police stations on Monday.
It is the first time a suicide bomber has truck at the Red Cross – famed for its neutrality – in its 140-year history.
The casualty toll makes it the bloodiest day in the Iraqi capital since Saddam Hussein’s regime fell to US-led forces in April. Most of the dead and injured were Iraqi civilians.
The ICRC has condemned the suicide car bombing which killed at least 10-people outside its HQ, saying they are angered and shocked by the blast.
Eyewitnesses say a white van that looked like an ambulance, crashed and exploded outside the building.
Car bombs exploded outside three police stations and a further attack was averted when police opened fire at suicide bomber, who failed to detonate his explosives.
Coalition officials say the man was carrying a Syrian passport, and that he has been captured.
No one has claimed responsibility for the bombings, but they came just a day after rockets were fired at the Rashid Hotel, leaving one US soldier dead and 17 people injured.
United Nations Secretary-General Kofi Annan has condemned in the strongest terms the attacks, describing the targeting of the ICRC as a crime against humanity.
Mr Annan says he has spoken to ICRC president Jakob Kellenberger to offer his deepest sympathy and condolences to families and loved ones of everyone killed or injured.
Meanwhile, rocket-propelled grenades have been fired on a US army post and a shop providing laundry services to US forces in the northern city of Kirkuk.
The shop was badly damaged, but no one was injured as it had been closed for Iftar, the meal breaking the day-long fast for Muslims at dusk during the holy month of Ramadan.