The attack was the bloodiest since December 1, 2005, when 10 US marines were killed and 11 wounded by a roadside bomb on the outskirts of the town of Falluja.
Tens of thousands of extra US and Iraqi troops have been deployed in Baghdad since February as part of the security crackdown.
Another US soldier was killed by a roadside bomb in the Diyala town of Muqdadiya on the same day, according to the US military.
In a separate attack on Monday, a suicide car bomber struck a gathering of senior police officials in Baquba, killing 10 policemen, including the city's police chief.
Raad Hameed al-Mula Jowad al-Tamimi, Diyala's governor, said: "This will not deter the work of the honourable and dedicated to bring about security, peace and prosperity."
The US plan to send 30,000 additional troops has reduced the number of sectarian murders in the capital, but there has been a surge in car bombings inside and outside Baghdad.
Ryan Crocker, the US ambassador to Iraq, in his first news conference since arriving in Baghdad, said he had been in discussions with the Iraqi government and US officials on how to "take apart" the car bomb cells which have defied the crackdown.
A wave of up to 15 explosions resounded in Baghdad before dawn on Tuesday, apparently coming from the city's outskirts.
Two more car bombs also exploded on Tuesday in a Baghdad car park outside the Iranian embassy and several Iraqi government buildings.