The Islamic State of Iraq and the Levant (ISIL) group has claimed responsibility for a late-night car bomb attack in Baghdad that killed at least 13 people, saying it was targeting a Shia armed group.

The two car bombs went off about 10 minutes apart late on Saturday in the Iraqi capital's Karrada district, known for its restaurants, cafes and ice cream parlours.

Police said the dead and wounded were mainly shoppers and people commemorating the anniversary of the death of Imam Ali, a key figure in Shia Islam. Two traffic policemen were among those killed.

The AP news agency put the number of dead higher at 19.

A statement claiming to be by the group was shared on Twitter claiming responsibility for the attacks. It said the group had targeted a gathering of Shia fighters, and had killed and injured close to a hundred people.

A police colonel told the AFP news agency that the attack had taken place near a popular restaurant in Karrada.

Sunday's claim of responsibility by ISIL is similar to previous claims this past week, in which the group characterised the attacks as a response to fighting in the western Anbar province.

Baghdad has seen a jump in car bombs in the last week.

The attacks on Saturday follow a wave of car bombings on Thursday, which killed 11 people and wounded more than 40.

Another nine people died in two car bombings in Baghdad on Monday.