The bombings, which hit Iraq the previous night, came as Iraqi forces battle IS in Mosul in a massive operation launched more than seven months ago to retake the country's second city from the jihadists.
In Baghdad, suicide car bombers attacked in the area of a checkpoint in the city's southern Abu Dsheer area, killing 24 people and wounding 20, Brigadier General Saad Maan told AFP.
Security forces were able to kill one of the attackers, but the second blew up his car bomb, Maan said.
IS issued a statement claiming the attack but gave a different account of how it unfolded, saying that one militant clashed with security forces using a light weapon before detonating an explosive belt, after which a second blew up a car bomb.
And in south Iraq, a suicide bomber blew up an explosives-rigged vehicle at a checkpoint on the outskirts of the city of Basra, killing 11 people and wounding 30, according to Riyadh Abdulamir, the head of Basra province health department.
Another militant who left a second explosives-rigged vehicle was killed by security forces, the Basra Operations Command said.
IS also claimed the Basra attack, but said that both bombs were successfully detonated.
The jihadist group overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes have since recaptured much of the territory they lost to the jihadists.
After recapturing the cities of Tikrit, Ramadi and Fallujah, Iraqi forces launched an operation to retake Mosul - at the time the largest population centre still in IS hands - last October.
