(adds hospital official, paragraphs 9 and 10)

BAGHDAD, Aug 14 (Reuters) - U.S. forces said they killed four people in a raid in Iraq's sprawling Shi'ite slum of Sadr City early on Tuesday, while relatives said the dead included a 5-year-old girl sleeping with her family on the roof.

Later in the morning, angry mourners marched through the slum's streets with flag-draped coffins.

Sadr City, home to about a third of Baghdad's six million people, has been a focus of American raids in recent weeks.

It is the main stronghold in the capital of Shi'ite militias loyal to cleric Moqtada al-Sadr, which Washington says are linked to Iran and were responsible for nearly three quarters of attacks against its troops in July.

"The Americans raided our house from the roof. They were jumping from one roof to another. They jumped on to our roof and killed my brother and my 5-year-old niece, Zahra Hassan," Ali Khamis Eidan, a policeman, told Reuters.

U.S. military spokesman Lieutenant-Colonel Christopher Garver said: "Our troops at the site did not inflict any casualties on civilians. The only people they fired at were people who fired at them."

Family members, including the girl's small brother, wept at the scene. On the roof blood had stained a mattress, where relatives said the girl had been killed. Many Iraqis sleep on their roofs in the summer to stay cool.

An official at Sadr City's Imam Ali hospital, Qasim Abdul Zahara, said the hospital's morgue had received three dead bodies, including a 5-year-old girl and her father, both killed by gun wounds to the head.

Four wounded were also treated at the hospital, including an elderly woman and her elderly husband, he added.

U.S. forces said Tuesday's pre-dawn raid was in pursuit of a "rogue" leader of Sadr's Mehdi Army whose militants had split from Sadr and had used "illicit materials smuggled from Iran" to carry out killings.

They said they captured eight suspects. Troops killed four militants after helicopters fired warning shots.

Last week U.S. forces said they killed about 30 militants in an air strike during a raid in Sadr City. They also mounted a raid on Sunday morning, in which they said they killed up to five people and captured 13.

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