They targeted three Baghdad neighbourhoods as well as Karbala and Basra provinces, south of the capital, the officials said.
In the Sadr City area of northern Baghdad, at least 15 people died and 34 were hurt when a suicide bomber detonated explosives inside a tent where local Shiite tribal leaders were meeting.
A car bomb struck another northern area of Baghdad, killing 13 people and wounding at least 24, while a roadside bomb in the capital's east killed two people and wounded three.
The violence came during a major offensive by Sunni jihadists that overran the entire province of Nineveh and swathes of Kirkuk to its southeast, and Salaheddin to its south.
The drive reached as far as the outskirts of Samarra, just 110 kilometres north of Baghdad, where clashes between security forces and militants ended without them entering the city.
Violence is running at its highest level since 2006-2007, the height of a brutal Sunni-Shiite sectarian war in which tens of thousands of people were killed.