Rockets hit Baghdad's heavily fortified "Green Zone", home to the prime minister's office and several Western embassies, on Tuesday and car bombs elsewhere in the capital killed 10 people, police and medical sources said.
One soldier was killed in the rare attack on the Green Zone, which is likely to heighten concerns about Iraq's ability to protect strategic sites as security deteriorates.
The car bombs struck mostly Shi'ite districts, including Shurta, in the southwest of Baghdad, where four people were killed in a crowded market, the police and medical sources said.
A car bomb in south Baghdad's al-Maalif neighbourhood killed two people and three died in a blast in the Bayaa quarter. In Taji, north of the capital, an explosion near a police patrol claimed another life, police said.
Police found the bullet-riddled bodies of two government-backed Sunni militiamen in Mishahda, north of Baghdad. Such fighters are often targeted by Sunni Islamist militants fighting Prime Minister Nuri al-Maliki's Shi'ite-led government.
No group immediately claimed responsibility for any of Tuesday's attacks.
Two years after U.S. troops departed, insurgents exploiting discontent among Iraq's alienated Sunni minority have rebounded, driving violence to an intensity not seen since the sectarian bloodshed of 2006-2007, when tens of thousands were killed.
The insurgents, led by the militant Islamic State of Iraq and the Levant, overran the western city of Falluja on Jan. 1. After a month-long standoff, the army has intensified shelling of the city since Sunday ahead of a possible ground assault.
More than 1,000 people were killed in violence in Iraq in January, according to monitoring group Iraq Body Count.