Police say the two blasts went off about 15 minutes apart in different parts of the city. Civilians and police are among the casualties.
The attacks come a day after at least 46 people were killed and some 200 others injured in a series of car bomb attacks in Baghdad.
Meanwhile, the U.S. military said that insurgents killed one U.S. soldier on March 12 in the western province of Anbar.
(AFP, Reuters)