The US military said on Wednesday: “Three soldiers assigned to 1st Brigade, 1st Armored Division died from enemy action while operating in Al-Anbar province today.”
A US Blackhawk helicopter also crashed in Anbar, leaving two US soldiers missing and four injured.
The crash did not appear to be due to hostile fire and the army is continuing to search for the missing soldiers, the American military said.
Al-Anbar has been the scene of the fiercest attacks by anti-US fighters.
The crash comes as the US attempts to regain full control of the Iraqi capital and quash an accelerating cycle of revenge killings by members of Iraq’s rival Sunni and Shia Muslim sects.
In the last few weeks 12,000 additional US soldiers have been re-deployed into Baghdad from north-western Iraq.
Five civilians died and 20 were hurt when a mortar shell exploded in a built-up district of Baquba, a mixed Sunni and Shia town north of Baghdad.
The attack collapsed a three-storey building near to a Shia mosque, police said. Witnesses feared some people were still trapped in the rubble.
Police said a bomb targeting a US patrol in east Baghdad had killed one civilian and injured another, while in Basra an Iraqi army colonel was shot dead on his way to work, the army said.
Two separate roadside bombs in Kirkuk also killed one civilian, wounded another and hurt three Iraqi soldiers.
The latest US attempt to restore government control over the Iraqi capital comes amid new evidence of rising and increasingly brutal violence.
In July almost 2,000 bodies were brought to Baghdad‘s morgue, an official there said on Wednesday.
Even Iraq’s mosques have become targets for militants
This is the highest number since early spring when a Sunni attack on a Shia shrine in the city of Samarra in February sparked a wave of sectarian bloodshed. The July toll of 1,815 was an increase from 1,595 in June.
Dr Abdul Razzaq al-Obaidi,the assistant manager of the Baghdad morgue, said that about 90% of the deaths were due to sectarian violence.
He said: “Most of the cases have gunshot wounds to the head. Some of them were strangled and others were beaten to death with clubs.”
The rising daily death toll has put new pressure on the American military to restore law and order to Baghdad.
Major-general James Thurman, commander of US-led forces in the Baghdad region, said: “We must dramatically reduce the level of violence in Baghdad that is fuelling sectarianism.
“Iraqi and US forces will help the citizens of Baghdad by reducing the violence that has plagued this city since the Samarra bombing.”
The US military also said it had arrested four Iraqi men in connection with the kidnapping of American journalist Jill Carroll, who was freed in March after 82 days in captivity.
Major-general William Caldwell said the four, who were not identified, were arrested in Anbar province west of Baghdad but he did not say when.
He said that Carroll, who worked for the Christian Science Monitor newspaper, was held 13km west of Fallujah.