The death of the woman, whose name was withheld, brought to 88 the number of American soldiers killed by hostile fire since President Bush declared an end to major combat operations May 1.
In downtown Baghdad, Iraqi police opened fire Wednesday after about 1,000 demonstrators demanding jobs stormed a police station, set fire to two cars and threw stones at officers, police said.
A similar incident occurred in the northern city of Mosul, where police fired warning shots in the air to disperse hundreds of unemployed Iraqis who marched to an employment office and the city hall to demand jobs. There were no reports of injuries in the protests in Mosul, Iraq's third largest city.
In other developments:
CBS News Correspondent Allen Pizzey reports the trouble in Baghdad began when police who used to guard foreign embassies and diplomatic residential areas came to try to get their old jobs back.
The protesters said they had been promised jobs in July, but the positions had not been given out. They charged the police were demanding bribes in return for hiring them.
One protester, Ali Hamid, 21, said he and others had applied for jobs as police but were refused even though they'd paid to get their names on the rolls of candidates.
"All these policemen are corrupt. We gave them money to register our names as candidates and when we returned they said we have no business being here. They are all corrupt from officers to regular policemen," Hamid said.
Ali Aboud, a 52-year-old out-of-work builder, said police had asked him to pay $100 for a job. He said such a sum was out of the question.
"They promised us they would give us jobs in July. We have come every week, but still we get no answer," Aboud said.
Another protester, Yassin Khudier claimed he paid a $100 to the driver of the chief of the Facilities Protection Force in order to get a job.
"I was deceived by this person (the driver) and I want my money back," added Khudeir.
Chief of the east Baghdad police Brig. Khadum Abide arrived to talk with the demonstrators and said appointments to the force would be announced on television in three days.
U.S. troops arrived at the scene of the violence about 45 minutes after the shooting broke out.
The shooting took place about three blocks north of the Palestine Hotel, home to much of the foreign journalist corps covering the U.S. occupation of the country.