The victims included Safa Mahmmod, the first female policeman to be killed in the current insurgency.
"Four vehicle-borne improvised explosive devices detonated in the Iraqi capital in the span of 90 minutes this morning," the statement said. "Initial reports indicate 26 people died in the blasts, with at least 21 more wounded."
Two Australian soldiers were among the wounded in the first car bombing that went off at approximately 7 am (0400 GMT) near the Australian Embassy.
At least one Iraqi was killed and "an unknown number of Iraqis were also wounded in the attack," the statement said.
Half an hour later, another car bombing took place near the Al Alahi Hospital in central Baghdad, leaving 18 people dead and 15 others wounded, according to the statement.
Around 8:15 a.m. (0515 GMT), two Iraqi security guards were killed, and three others wounded in a third car bomb blast, southwest of the Baghdad International Airport, the statement added.
The fourth car bombing came at 8:30 a.m. (0530 GMT) near the Muthana Airfield, killing two Iraqi soldiers and two civilians, the statement said, adding that one US soldier was also wounded.
However, "despite loss of life, none of the suicide bombers hit their intended targets," the statement said.
Radicals bent on disrupting the January 30 polls have stepped up attacks d attacks against US forces, Iraqi police, national guards as well as civilians working for foreign forces.
But the UN and the US assert that the elections will be held as scheduled.