Two busy commercial areas in Baghdad were hit by car bombings, with one of the attacks occurring at about 1.00 a.m. (local time) when one of the group's suicide bombers, detonated his car bomb at a crowded thoroughfare in Karrada-Dakhil district, Xinhua news agency reported.

The powerful blast set fire to five nearby buildings and several shops, and destroyed many stalls and civilian cars at the scene which was crowded with shoppers who were preparing their families for Eid ul-Fitr.

Baghdad was the scene of another post-midnight attack when a booby-trapped car blew up at another popular market in Baghdad's Shaab district, killing a civilian and wounding five others, the local media reported.

Iraqi Prime Minister Haider al-Abadi vowed to punish the terrorists behind the attacks.

"The terrorist groups carried out such desperate deadly attacks as a result of being crushed in the battlefield," an official said, referring to the latest defeat of the IS in the country's Anbar province, including its stronghold in Fallujah.