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.
ISIS claimed the attack, 30 km east of the Shiite 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 US-backed Iraqi offensive launched in October.
The group is also on the backfoot in neighboring Syria, retreating in the face of a US-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.
ISIS declared a self-styled “caliphate” over parts of Syria and Iraq three years ago.
Woman suicide bomber kills at least 30 in Iraqi market