Bombs and bullets killed at least 11 other people, including four Marines who died in a pair of bombings in western Anbar province.
Sheik Kamal Nazal, a Sunni preacher and chairman of the Fallujah city council, was gunned down in a hail of bullets from two passing cars as he walked to work, police Chief Brig. Hudairi al-Janabi said.
No group claimed responsibility for the killing, which occurred in one of the most tightly controlled cities in Iraq. However, it appeared part of a campaign of intimidation by Sunni insurgents against Sunni Arabs interested in promoting a political settlement to stem the violence.
Last month, Nazal welcomed Prime Minister Ibrahim al-Jaafari and U.S. Ambassador Zalmay Khalilzad to the city 40 miles west of Baghdad.
U.S. officials have been working hard to encourage Sunni Arabs to abandon the insurgency, and have been urging Shiite and Kurdish leaders to give major government posts to the disaffected minority.
Shiite officials concede some in their ranks may be guilty, but months of investigations have failed to yield a single arrest, CBS News correspondent Kimberly Dozier reports from Baghdad.
American diplomats and military commanders believe that strategy offers the best way to calm the insurgency so U.S. and other international troops can begin heading home.
In other recent developments:
U.S. authorities arranged a meeting with local Sunni leaders in Ramadi on Nov. 28 as a major step in a political dialogue. But a suicide attack Jan. 5 against Sunni police recruits in the city, which is about 30 miles from Fallujah, set back the process. Nearly 60 people were killed, including two Americans.
A senior member of the Iraqi Islamic Party, a Sunni political group seeking a place in the new government, deplored Tuesday's assassination and blamed U.S. and Iraqi authorities in part for failing to protect the sheik.
"Those who wanted to eliminate Sheik Nazal are aimed at bringing more instability to the city," Dr. Salman al-Jumaili said. "We hold the Iraqi government and occupation forces responsible for bringing all this suffering and damage to this city."
The Shiites insist the claims they are involved are exaggerated, and they say at least as many Shiites are being killed as Sunnis. But Sunnis are seeing red, and they want payback, Dozier reports, adding, Sunnis were the backbone of the insurgency. By last fall, Americans had talked many of them into joining politics and taking on al Qaeda in Iraq. Now, some are forming new armed groups, turning their energies toward fighting the Shiites.
Fallujah was the major stronghold of insurgent and religious extremists, including al Qaeda in Iraq, until the city fell to a U.S. air and ground assault in November 2004. Fallujah since has become one of the most intensely guarded cities in the nation.