The first blast was near a local government building and the second one about 60 metres (65 yards) away at a bus station, police sources said. The death toll was expected to keep rising.
Unverified online photographs showed a large plume of smoke rising above the buildings as well as burnt out cars and bodies on the ground at the site of one of the blasts, including several children. Police and firefighters carried victims on stretchers and in their arms.
Islamic State said it had attacked a gathering of special forces in Samawah, 230 km (140 miles) south of the capital, with one car bomb and then blew up the second when security forces responded to the site.
Islamic State holds positions mostly in Sunni areas of the country’s north and west, far from the mainly Shi’ite southern provinces where Samawah is located. Such attacks are relatively rare.
The rise of the ultra-hardline Sunni insurgents has exacerbated Iraq’s sectarian conflict, mostly between Shi’ites and Sunnis, which emerged after the 2003 U.S.-led invasion that toppled Saddam Hussein.
The quota-based governing system putin place by the United States at the time is being challenged by hundreds of protesters who camped out overnight in Baghdad’s heavily fortified Green Zone after storming the parliament building.