A female suicide bomber detonated her explosive belt in a market in the town of Musayyib, south of Baghdad, on Friday killing at least 30 people, Iraqi security sources said.

At least 35 other people were wounded in the attack in the centre of Musayyib, a town that lies about 60 kilometres south of the capital, a police officer and a medic at the local hospital said.

The attack in Musayyib came hours after another, apparently failed attack in Karbala, in which four civilians were wounded when a suicide bomber blew himself up at the entrance of the city's main bus station early Friday, police sources said.

Both attacks were claimed by the militant Islamic State (IS) group through its propaganda agency Amaq.

The IS has carried out dozens of deadly suicide bombings targeting civilians but Iraq has been on heightened alert since the start of Ramazan.

More than 40 people were killed and dozens wounded in a spate of attacks on May 30, a few days after the beginning of Ramazan, including a devastating blast at an ice cream shop in central Baghdad's Karrada neighbourhood.

The bombings in Baghdad come as Iraqi forces fight to retake the last IS-held areas of Mosul, a city that was the militant group's emblematic stronghold.

Iraqi forces are almost eight months into a massive operation to recapture the second city and have already taken back its whole eastern side and much of the west.