The bold daylight kidnapping came as the top U.S. commander in Iraq said the threat from the terror network has been "significantly reduced" in the capital.
A suicide car bomber, meanwhile, struck a busy commercial area in the oil-rich, northern city of Kirkuk, killing at least eight people and wounding 26, police said.
The two cars carrying the sheiks -- seven Sunnis and three Shiites -- were ambushed in Baghdad's predominantly Shiite neighborhood of Shaab about 3:30 p.m., police officials said.
The sheiks were returning to Diyala province after attending a meeting with the Shiite-dominated government's adviser for tribal affairs to discuss coordinating efforts against al-Qaida in Iraq, police and a relative said.
Police found the bullet-riddled body of one of the Sunni sheiks, Mishaan Hilan, about 50 yards away from where the ambush took place, an officer said, adding that the victim was identified after his cell phone was found on him.
A relative of one of the abducted Shiite sheiks blamed Sunni extremists and said the attackers picked a Shiite neighborhood to "create strife between Shiite and Sunni tribes that have united against al-Qaida in the area."
But, Jassim Zeidan al-Anbaqi said, "this will not happen."
The well-planned attack was the latest to target anti-al-Qaida tribal leaders and other officials in an apparent bid to intimidate them from joining the U.S.-sponsored grass roots strategy that the military says has contributed to a recent drop in violence.
Gen. David Petraeus, the top U.S. commander in Iraq, said Sunday that the threat from al-Qaida in several former strongholds in Baghdad has been "significantly reduced" but the group remains "a very dangerous and very lethal enemy."
He singled out success in what had been some of the most volatile Sunni neighborhoods in Baghdad, including Ghazaliyah, Amariyah, Azamiyah and Dora.
"Having said that ... al-Qaida remains a very dangerous and very lethal enemy of Iraq," he said. "We must maintain contact with them and not allow them to establish sanctuaries or re-establish sanctuaries in places where they were before."
In all, at least 35 people were killed or found dead across the nation, including the decomposing bodies of 12 Shiites found near the Diyala provincial capital of Baqouba, an army officer said.
An explosives-laden car also exploded near a market in Baghdad's northern Shiite district of Kazimiyah, killing at least two civilians and wounding 10, according to local police
The suicide bombing in Kirkuk, 80 miles north of Baghdad, struck a mainly Kurdish area in the city, which has seen a rise in ethnic tensions as Iraq's Kurds try to strengthen their presence there as a prelude to annexing it to their nearby self-rule region.
The city's Arab and Turkomen residents dispute the Kurdish claim.