US marines in western Iraq have launched a new offensive against what they say are al-Qaeda fighters.
An attacker targeted a key entrance to Baghdad's Green Zone
The offensive, in towns along the Euphrates valley, Haditha, Haqlaniya and Barwana, has been named Operation River Gate.
About 2,500 US troops, as well as Iraqi forces, are taking part, backed up by helicopters and war planes.
But as the operation got under way, the US military announced four of its troops had been killed in the area.
Three of them were killed in a bomb attack in Haqlaniya on Monday, and a fourth, a marine, was killed on the Syrian border, said the statement.
Meanwhile, in Baghdad, a suicide car bomb exploded at a main entrance into the Green Zone, which houses Iraq's parliament as well as the US embassy.
Three Iraqis - at least two of them police officers - were killed and around six people wounded, officials said.
In other developments:
- US and Iraqi forces, backed by armoured vehicles and helicopters, clash with some 40 rebels near Yusufiyah, south of Baghdad, reports the AFP news agency
- Iraq's Central Criminal Court sentences 28 people, including two Saudis, a Yemeni and an Algerian, to prison terms for carrying out terrorist crimes in Iraq, says the Associated Press
The attack in Baghdad came on the day Iraqis marked the start of the Muslim holy month of Ramadan.
On Tuesday, al-Qaeda in Iraq purportedly urged Sunni Muslims to step up attacks against US and Iraqi forces during Ramadan.
The statement on an Islamic website also urged them to boycott the referendum on the constitution in 11 days time.
Sunni Arabs reacted angrily on Tuesday to changes to referendum voting arrangements by Iraq's Shia-dominated parliament, making it harder to reject the constitution.
Now, the two-thirds majority needed in three provinces to defeat the constitution will only be counted from all registered - as opposed to actual - voters.
Many registered voters may not show up because of the violence, Sunni opponents argue.
The US military says Operation River Gate aims to "free local citizens of the terrorists' campaign of murder and intimidation".
The towns targeted by the operation are among several in the Euphrates valley area where local people say fighters have taken control and imposed Taleban-like Islamic rule, despite frequent operations by US and Iraqi forces.
Another operation launched on Saturday, called Iron Fist, continues further west, near Iraq's border with Syria.
US officials say soldiers backed by fighter aircraft and helicopter gunships have killed at least 33 rebels since the start of the operation.
Meanwhile, US and Iraqi forces have been fighting insurgents in the town of Ramadi, 110km (70 miles) west of Baghdad.
Clashes broke out after an Iraqi army patrol was attacked. At least five gunmen are reported to have been killed.