Harith Dhaher al-Dhari died when gunmen fired rocket propelled grenades on his car in the Abu Ghraib district, according to a district official who spoke on condition of anonymity because he feared reprisals.
The official said a passenger traveling with al-Dhari also was killed as well as another associate in a second car traveling behind. He blamed Al Qaeda in Iraq for the attack, but did not say how he arrived at that conclusion.
The group, in a statement posted on the Internet said: "The 1920 Brigades mourns its martyr, the brave leader Harith Dhaher Khamis al-Dhari who fell today, his honorable blood spilled on the battlefield of his jihad (holy struggle) in Abu Ghraib."
The authenticity of the brief statement could not be verified but it appeared on a site that routinely publishes militant literature.
The killing of al-Dhari is likely to deepen the increasingly bloody rift between government supporters and opponents of Al Qaeda in the Sunni Arab communities west of Baghdad.
The attack took place at a time when the Shiite-led government of Prime Minister Nouri al-Maliki was making progress rallying tribesmen in the Anbar province, the epicenter of the Sunni insurgency, behind it in the fight against Al Qaeda, the deadliest terror group in Iraq.
The government-backed tribal militias have been trying to chase Al Qaeda fighters out of the vast Anbar province. Al Qaeda has responded with bomb attacks targeting leaders and key supporters of the tribes allied against them.
The killing of the insurgent leader also came one day after outgoing U.S. Ambassador Zalmay Khalilzad told reporters that American and Iraqi officials had talked to representatives of insurgent groups hoping to draw more Sunni groups away from Al Qaeda.
The 1920 Revolution Brigades has consistently been rumored to have taken part in these secret talks, which are believed to have been deadlocked over the demand that insurgents to lay down their arms and join the political process.
Al-Dhari's father is the sheik of al-Zuba'a tribe in Abu Ghraib. Also a member of this tribe is Deputy Prime Minister Salam al-Zubaie, who was seriously wounded Friday when a suicide bomber blew up his vest of explosives at the prayer room of his Baghdad home.
The Islamic State in Iraq, an Al Qaeda-linked group, claimed responsibility for the attack on al-Zubaie, which killed nine people.
In separate statements, al-Dhari was mourned by the Iraqi Islamic Party, the country's largest Sunni Arab party, and by the Association of Muslim Scholars, a radical Sunni group led by Harith al-Dhari, an uncle of the deceased al-Dhari.
Both groups have long been suspected of maintaining links to Sunni Arab groups fighting U.S. and Iraqi forces since 2003. The Islamic Party, however, is widely viewed as a force of moderation within the Sunni Arab minority, which is deeply embittered by the loss of its domination under Saddam Hussein. The association, on the other hand, has grown increasingly militant.
"To be associated with the insurgency is an honor," the surviving al-Dhari told a television interviewer earlier this week. "We believe it trusts the association when it comes to working toward forcing the occupiers out."