Kerbala - A woman detonated her explosive belt in a market east of the holy city of Kerbala on Friday, killing at least 30 and wounding 35, Iraqi security sources said.

Islamic State claimed the attack in the town of Musayab, south of Baghdad, in a statement on its Amaq news agency. It didn't identify the bomber.

A security officer said the assailant was a woman who hid the bomb under the customary full-body veil.

The attack comes as Islamic State is about to lose Mosul, the de-facto capital of the hardline group in Iraq, to a U.S.-backed Iraqi offensive launched in October.

The group is also on the backfoot in neighboring Syria, retreating in the face of a U.S.-backed Kurdish-led coalition attacking its capital there, Raqqa,.

Iranian-backed paramilitaries are taking part in the campaign fighting Islamic State in Iraq, attacking the group in the border region near Syria.

Islamic State declared a self-styled "caliphate" over parts of Syria and Iraq three years ago.

According to AFP, a suicide bomber blew himself up in a market in the town of Musayyib, south of Baghdad, on Friday killing at least 20 people, medical and security sources said.

"A suicide bomber blew himself up in Musayyib market, causing 20 civilian martyrs," an interior ministry spokesman said.

At least 34 other people were wounded in the attack in the centre of Musayyib, a town that lies about 60 kilometres (35 miles) south of the capital, a police officer and a medic at the local hospital said.

A source at Musayyib hospital said at least four of the wounded were in very serious condition following the blast, which rocked the market at around 11:30 am (0830 GMT).

The attack in Musayyib came hours after another, apparently failed attack in the Shiite shrine city of Karbala, a few kilometres (couple of miles) to the southwest.

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 Islamic State militant group through its propaganda agency Amaq, which in both cases spoke of a "martyrdom-seeking operation" using an explosive vest. IS has carried out dozens of deadly suicide bombings targeting civilians but Iraq has been on heightened alert since the start of the holy Muslim fasting month of Ramadan.

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

It was during Ramadan last year that IS carried out its deadliest ever attack in the Iraqi capital with a truck bomb that set two shopping arcades ablaze, also in Karrada, resulting in more than 320 deaths.

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.