A car packed with explosive blew up in al-Jadeeda (New Baghdad), an eastern district of the capital, killing at least 15 people and wounding over 50, a police officer said.
A suicide car bomb also targeted a main army checkpoint in Taji, just north of Baghdad, killing seven soldiers and wounding more than 20 others, he said.
The attacks come as Iraqi forces are trying to dislodge Islamic State (ISIS) militants from Falluja, their stronghold just west of Baghdad.
So far, ISIS has not claimed the attack but analysts argue there is evidence they are responsible.