(Adds quotes from U.S. colonel in Ramadi, paragraphs 9-12)

By Ross Colvin

BAGHDAD, Aug 3 (Reuters) - Four U.S. soldiers were killed in Baghdad, the U.S. military said on Friday, underlining U.S. President George W. Bush's grim prediction of "a very difficult August" for U.S. troops in Iraq.

The military said a roadside bomb killed three soldiers on patrol in eastern Baghdad on Thursday during operations targeting Shi'ite and Sunni militants. Eleven others were wounded. A fourth soldier died in combat in a western district.

Bush has sent an extra 30,000 troops to Iraq, despite strong opposition at home, to help quell unrelenting sectarian violence and give Iraq's leaders time to achieve a political deal to promote national reconciliation.

His strategy has had some success but at a cost -- May was the deadliest month in 2 1/2 years for U.S. troops with 126 killed, and more than 100 died in both April and June.

The July death toll, initially put at 74, was welcomed by U.S. commanders as a possible sign the military buildup was bearing fruit. But by Friday, the toll had climbed to 81 on the icasualties.org Web site, on a par with February and March.

In May, Bush predicted that Iraqi militants, particularly Sunni Islamist al Qaeda, would attempt to influence the U.S. debate on the war by launching attacks ahead of a military assessment of the strategy due in September.

"It could be a bloody ... it could be a very difficult August," he said. Five U.S. soldiers died in the first two days of the month.

The biggest killer of U.S. troops is roadside bombs, which Washington says neighboring Shi'ite Muslim Iran supplies to Shi'ite militant groups in Iraq.

The U.S. Army painted a slightly more optimistic picture in the Anbar capital of Ramadi. Army Col. John Charlton, commander of the 1st Brigade, 3rd Infantry Division, said daily attacks in Ramadi fell from 30 to 35 in February to one a day thanks largely to the growth of local police and army units.

Anbar had been an al Qaeda stronghold where Sunni tribal leaders have turned against militants in recent months.

Charlton, who commands an area of about 500,000 residents centered on Ramadi, said local forces continued to depend on the United States for fuel, weapons and ammunition.

"I think probably in the next six to eight months we ought to be able to get a lot of those (logistics) systems in place," Charlton said at a Pentagon briefing via video link from Iraq.

BROTHERS MOURNED

Tens of thousands of Iraqis have died in the violence, victims of a wave of sectarian violence and criminal gangs taking advantage of a security vacuum.

In the northern city of Kirkuk, relatives mourned the deaths of five brothers who were kidnapped and killed after their desperately poor family was unable to pay a $100,000 ransom.

Police found a sixth brother, a small boy, weeping but unharmed next to the bodies, which had been bound and shot in the head. Many such murders take place every day in Iraq, but the presence of the small boy at the scene touched a nerve.

Reuters pictures showed an uncle of one of the men, turbaned and wearing white traditional Arab robes, weeping and curled up next to a wooden coffin, the body of his nephew wrapped in a thick patterned blanket.

A cousin of the men said four of them, all day laborers, had gone to help their brother paint the hospital in al-Rashaad district southwest of Kirkuk.

On their way home to Kirkuk, they were kidnapped by gunmen. When the family said they could not afford to pay the ransom, they were told, "Then come and get their bodies."

In other violence, gunmen in the southern holy Shi'ite city of Najaf killed an imam with links to reclusive spiritual leader Grand Ayatollah Ali al-Sistani, in a drive-by shooting. (Additional reporting by David Morgan)

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