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 districts 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 neighborhood 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 regime-backed Sunni militiamen in Mishahda, north of Baghdad.

No group immediately claimed responsibility for any of Tuesday's attacks.

More than 1,000 people were killed in violence in Iraq in January, according to monitoring group Iraq Body Count.