The bombings near the Kirkuk offices of the Patriotic Union of Kurdistan (PUK) and a local council in Ramadi on Thursday appeared to target the US-led occupation.
A huge explosion threw up a cloud of black smoke, shaking buildings across town. The blast flattened a wall around the green-painted headquarters of the PUK and shattered windows at a nearby primary school, wounding several children.
The dead included a school employee, two children and a man.
"I was walking in the street when a car exploded," said
Hussein Ali, 52. "I didn't know if it was night or day."
Meanwhile, one US soldier was killed and two wounded when a military convoy was hit by a roadside bomb near Ramadi, a US military spokesman said.
Earlier on Thursday, three US soldiers on were wounded when their convoy struck a roadside bomb near a bridge in Shalchiyah district in central Baghdad.
Late on Wednesday, a car bomb blast struck near the offices of a the local council in Ramadi, west of Baghdad. Local officials said two people were killed and 11 were wounded, including the council leader.
Blast in Kirkuk was felt across
Witnesses said a car laden with explosives was detonated by the driver.
In the capital on Thursday a gunman shot dead an Iraqi policeman guarding the Jordanian embassy. The mission moved to new premises after it was devastated in an August bomb attack.
Speaking from Britain, US President George Bush said he could increase the number of US troops in Iraq, a statement that contrasts with Pentagon plans to reduce deployment ahead of the 2004 US presidential election.
Speaking at a news conference with British Prime Minister Tony Blair, Bush promised to "finish the job we have begun."
"We could have less troops in Iraq. We could have the same number of troops in Iraq. We could have more troops in Iraq, (whatever is) necessary to secure Iraq," Bush said.
Bush said he would rely on his commanders on the ground to determine how many troops are needed in Iraq, where resistance attacks on US forces and international targets have become increasingly sophisticated and deadly since US forces ousted Saddam Hussein in April.