A police officer said two parked explosives-laden cars detonated within minutes of each other, around midday in the southern Iraqi city of Samawah.
The first car exploded near government offices, while the second exploded minutes later at an open-air bus station about 60 metres away.
The officer said he expected the death toll to rise.
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.
Isis primarily holds positions in Sunni areas of the country's north and west, far from the mainly Shia southern provincies were Samawa is located. Such attacks are relatively rare.
The terror group claimed resonsibility for a bombing that killed at least 21 people and wounded many more, in an attack targeting Shia pilgrims on Saturday morning.
A state of emergency was declared in the capital as the unrest continued on Saturday afternoon. Security officials said entrances to the city had been shut as a "precautionary measure".
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