Hilla: A woman suicide bomber killed at least 31 people and wounded 35 in a crowded market in the town of Musayab, 80 km (50 miles) south of Baghdad, on Friday, security sources said.
Islamic State claimed the attack, 30 km east of the Shi`ite holy city of Kerbala, as well as a suicide attack at a bus station in central Kerbala around the same time. It did not identify either bomber, in a statement on its Amaq news agency.
Security sources said four people were wounded in the Kerbala bombing, and one security officer said the bomber was also a woman and had hidden the bomb under her full-body veil.
The hardline Sunni Muslim insurgents are on the brink of losing Mosul, their de-facto capital in Iraq, to a U.S.-backed Iraqi offensive launched in October.
The group is also on the backfoot in neighbouring Syria, retreating in the face of a U.S.-backed, Kurdish-led military coalition attacking Raqqa, its capital there.
Iranian-backed paramilitaries are taking part in the campaign against 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.