The fifth soldier died of wounds suffered in the offensive named Operation Iron Fist, which continues into its fourth day on Wednesday.
Up to 2500 troops have been deployed for the military action.
Three soldiers were killed by improvised bombs in Haqlaniya, in the western Anbar province on Monday, the US military said.
In Karabila, near the Syrian border, one marine was killed by an improvised bomb, during a military operation there called Iron Fist.
Iraqi National Assembly speaker Hajim al-Hasani denounced the US military operations, saying they discourage Iraqis from participating in the referendum on the new constitution.
Hajim al-Hasani denounced
”Frankly, I am against these operations,” he told Aljazeera.
“In this respect, I have called before these attacks for halting these operations so that people will not believe the attacks are aimed at preventing them from participating in the referendum,” al-Hasani said.
“There must be alternative solutions instead of later talking about low turnout for the referendum, just like what occurred in the elections,” he said.
Operation River Gate
The west Iraq offensive is part of an overall operation called Hunter, which the US military said sought to deny al-Qaida the ability to operate freely in the Euphrates River valley and to “prevent terrorists from influencing the local population through murder and intimidation”.
Hundreds of troops are deployed
In Operation River Gate, which was launched on Tuesday, about 2500 troops have been scouring three towns along the river, west of Baghdad.
A combined force of 900 US and Iraqi troops are working in Operation Mountaineers around the area of Ramadi, also west of the capital, to secure it ahead of the 15 October referendum on the constitution.
British national released
Iraqi police on Tuesday released a British national who had been arrested in southern Iraq, officials said.
The man, Colin Peter Wanley, was taken into custody by Iraqi authorities on Monday, and British officials were looking into the case, Britain’s Defence Ministry said in London.
Colin Peter Wanley was travelling
Sadoun al-Jabiri, a spokesman for the Iraqi border police in Najaf, said Wanley, an engineer, and 10 Iraqis were carrying weapons and surveillance equipment in several vehicles when police stopped them on a road between the Saudi border and the Iraqi city of Najaf.
Al-Jabiri said Wanley was taken into custody because he had entered Iraq without a required visa.
The 10 Iraqis, too, were arrested, and the 11 men appeared in court in Najaf on Tuesday, said al-Jabiri and Major General Hussein al-Ghazali, the commander of the area’s border police.
After reviewing his documents, the court freed Wanley, said al-Jabiri and al-Ghazali.
The court also released three of the guards after examining their weapon licences, and was expected to do the same in another hearing on Wednesday.
Najaf, a mostly Shia city is about 200km east of the Saudi border and about 160km south of Baghdad.