In the first attack, a car sped towards an entrance to the Green Zone, which houses the interim government, but blew up near a recruitment booth for the Iraqi National Guard metres away from the gate.
Reports said most of the dead and wounded were civilian passersby.
As rescue workers and paramedics struggled to cope, a huge explosion rocked the street half an hour later outside the Baghdad hotel, where US and other foreign workers and experts and government personnel are usually housed.
The explosion occurred as a convoy of US military vehicles was passing through the main street.
US forces sealed off the area, and there were no immediate reports of casualties.
The explosions came a day after American forces regained tenuous control of the rebel stronghold of Samarra, 60 km north of Baghdad, and continued airstrikes on selected targets in the city of Fallujah in the west.
US officials said the 1 am airstrike attack on a couple of houses in Falluja came after 10 to 15 rebel fighters were spotted carrying weapons to the buildings, and "a large number of enemy fighters are presumed dead."
The airstrike sparked of massive secondary explosions, indicating that the houses were being used as arms dumps, a spokesman said.
Other agencies, however, said the victims were mostly innocent women and children.
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