At least 17 people have been killed and 15 others wounded in two separate car bomb attacks in the Iraqi capital Baghdad, police and medics have said.

The first blast on Thursday went off in the city's eastern al-Obeidi area during the morning rush at a food market, killing seven civilians and two policemen, and wounding 15. The Islamic State of Iraq and the Levant (ISIL) armed group has claimed responsibility for the attack.

Just hours later, a second explosion hit the central Baghdad district of Bab al-Moadham near a security checkpoint, killing eight. There has been no claim of responsibility for the second attack.

Both bombs had been left in parked vehicles.

Elsewhere, four attacks in and around Baghdad killed at least seven people, bringing Thursday's overall death toll to at least 21.

Those attacks, mostly by bombs that went off in commercial areas or targeted security forces, wounded at least 20 people.

The blasts bore the hallmark of ISIL (also known as ISIS), which has carried out a string of bombings in Baghdad over the past week, killing nearly 100 people.

On Tuesday, ISIL claimed a suicide car bombing at a busy market in the Sadr City district, killing at least 39 Iraqis.

At least 28 people were killed and 54 others wounded in a double bombing in the centre of the city on Saturday, carried out by ISIL.

Baghdad has been on high alert since October 17, the start of Iraq's largest military operation since the 2003 US invasion to retake the northern city of Mosul, which was captured by ISIL in 2014.