The 65-year-old Sunni sheikh was the fourth city council chairman to be killed in some 14 months as fighters target fellow Sunnis willing to co-operate with the US and its Iraqi partners.
"The chances of success [in Iraq] are essentially zero because the Iraqi people have no voice"
Non Sequitur, Cadiz, Spain
Send us your views
The US military confirmed the killing and provincial officials condemned it.
"He was one of the many good people of the province who worked to help the city of Falluja rebuild and regain life," the provincial government said in a statement.
"This murder was a crime against all of the citizens of Iraq. We again strongly condemn this cowardly back-stabbing act."
Fellow councilmen and neighbours said Abdul-Amir had run for the office before and ignored pleas from friends not to take the job because of the dangers involved.
Abdul-Amir's predecessor, Abbas Ali Hussein, who was shot to death on February 2.
Critics of al-Qaeda
Both men were strong critics of al-Qaeda in Iraq, which is battling a growing number of Sunni tribes that have turned against it in the vast Anbar province - a centre for anti-US militias since the uprising in Falluja in 2004 that galvanised the insurgency.
The attack comes as American officials have increasingly expressed optimism about efforts to tame Anbar, having struck alliances with influential Sunni sheikhs once arrayed against American-led forces.
The tribes are competing with al-Qaeda for influence and control over diminishing territory in the face of US assaults.
On September 24, 2006, armed men broke into the home of Najim Abdullah Suod, the city council chief who preceded Hussein, killing the lawyer and his 23-year-old son, while Sheikh Kamal Nazal, a cleric, was shot down as he walked to work on February 7, 2006.
At least 38 people were killed or found dead elsewhere in Iraq, including another top city official, the mayor of Mussayyib who died in a roadside bombing in the city about 60km south of Baghdad.
Three US soldiers were killed and six others were wounded on Saturday in separate attacks in Baghdad and southwest of the capital, the military said.
|US soldiers face daily attacks during foot|
patrol in different parts of Baghdad [AFP]
A roadside bomb killed one US soldier and wounded two while they were on a foot patrol southwest of Baghdad, the military said.
Another soldier died and three were wounded when their vehicle was struck by a roadside bomb, followed by small-arms fire in southwestern Baghdad, the military said separately.
A combat security patrol also was attacked by small-arms fire, killing a soldier and wounding another in an eastern section of the capital, the military said.
Also on Saturday, Poland's defence ministry said a Polish soldier was killed and four others were injured when their convoy was hit by a roadside bomb on Friday night in Diwaniya, 130km south of Baghdad.
Prime minister's tour
Nuri al-Maliki, the Iraqi prime minister, meanwhile, prepared to begin an Arab tour on Sunday that will take him to Egypt, Kuwait, the UAE and Oman, his adviser Yassin Majid said.
Al-Maliki will start with a visit to Egypt, the Arab world's most-populous nation, where he will meet with Hosni Mubarak, the president, and other senior officials, Majid said.
The visit comes 10 days before two conferences on Iraq in the Egyptian Red Sea resort of Sharm el-Sheik.
Those will be attended by Iraq's neighbours as well as Bahrain and Egypt, and delegates from the five permanent members of the UN Security Council - the US, Russia, China, France and Britain.