At least 28 people were killed in a series of suicide bombings in central Baghdad on Monday, the first day of the Muslim holy month of Ramzan.
The targets were the International Committee of the Red Cross headquarters and four police stations.
The first bomb appeared to have been packed into an ambulance, which exploded as it entered the gates of Red Cross building.
"There are intelligence indicators that these attacks seem to have the mode of operations of foreign fighters," the BBC quoted a US military spokesman, Brigadier General Mark Hertling, as saying.
Grey smoke billowed over Red Cross building, as ambulances rushed to the scene and helicopters circled overhead.
Twelve people died in the attack, the Red Cross said. Witnesses said the driver of the vehicle that exploded was among the dead.
At least 16 people died and 94 were wounded in the attacks on three police stations, Baghdad Police Chief Major Bassem Alani said. An attempt on a fourth station was thwarted. In that attempt, Iraqi police said they wounded a Syrian and took him into custody.
The Red Cross expressed dismay at the bombing.
"We are deeply shocked... because it is an attack against the ICRCÂ… and that means, of course, a deliberate attack against our protective emblem and against our work," said chief spokeswoman Antonella Notari at the organisation's Geneva headquarters.
A spokeswoman in Baghdad said she could not understand why the Red Cross had been targeted after two decades of humanitarian work in Iraq.
