The latest violence followed a series of car bombs late Wednesday, including four that exploded within minutes of one another. At least 23 people were killed in western Baghdad's Shula neighborhood and a nearby suburb.
The Web statement said Abdullah Mohammed Rashid al-Roshoud was killed in fighting near Qaim, on the border with Syria. It was signed by Abu Musab al-Zarqawi, the most notorious terrorist leader in Iraq.
The statement did not say when al-Roshoud was killed, but US forces have launched a series of offensives near Qaim in past weeks against militants coming across the border.
Al-Roshoud slipped into Iraq in April, according to the posting, the authenticity of which could not be confirmed.
The Saudi militant and a group of mujahedeen "killed some of the Crusaders until the enemies of God had to withdraw."
"When the Crusaders could not enter the area, the only thing they could do was bombard the mujahedeen with warplanes," it said. "Our sheik (al-Roshoud) got what he wished" -- martyrdom.
Al-Roshoud had been No. 24 on a list of the 26 most-wanted terrorist leaders put out by Saudi Arabia two years ago and was one of only three militants on the list still at large. He was one of the main theologians for al-Qaida's network in Saudi Arabia, calling for a holy war against the Saudi royal family and Western interests in the Persian Gulf.
The bombings Wednesday and Thursday served as a chilling reminder of how potent militants remain in the capital despite around-the-clock patrols by American and Iraqi troops.
Most residents of the two Baghdad neighborhoods that were attacked are from Iraq's Shia majority, while the insurgents are almost exclusively Sunni Arabs, a minority that dominated Iraq until Saddam Hussein's ouster two years ago.
The explosions both days were carried out at times when large crowds were on the capital's streets.
Wednesday night's bombs came hours before an 11 p.m. curfew, when many residents are out at eateries or chatting
Thursday's twin explosions took place when many are just beginning their daily routines. Five police officers were among the 15 dead.
A young boy, his left leg missing from below the knee, sat on the sidewalk near a mangled bicycle, screaming as a man tried to comfort him. The force of the blasts blew off store shutters, and the surrounding sidewalks were covered with debris, including shattered glass, concrete slabs and charred vegetables and fruit.
A few trees were toppled, scattering leaves on the sidewalk.
Separately, a car bomb detonated by remote control hit an Iraqi police patrol in Tuz Khormato, north of Baghdad, killing one policeman and wounding seven civilians, police Brig. Gen. Sarhad Qadr said. Tuz Khormato is 55 miles south of the northern city of Kirkuk.
In another incident before dawn Thursday, US troops backed by Iraqi troops and helicopters killed seven insurgents who opened fire on the patrol from a home in western Baghdad's Jamiaa neighborhood, said police Maj. Moussa Abdul Karim and 1st Lt. Mohammed al-Heyaali.
The home was reduced to rubble and US troops standing in front displayed a weapons cache they had seized, including rocket-propelled grenade launchers, machine guns and ammunition.
Iraqi police, meanwhile, detained 50 suspected insurgents in separate raids in southeastern Baghdad and north of the capital Thursday, officials said.
Insurgents bent on starting a civil war to overthrow Iraq's US-backed government have maintained nearly eight weeks of relentless attacks, killing more than 1,240 people since April 28, when Prime Minister Ibrahim al-Jaafari announced his Shia-dominated government.
Sunni Arabs, who dominated Iraq for decades, lost power when Saddam, their last patron and a Sunni, was ousted. Their boycott of historic elections in January further sidelined them.
But Sunni Arab participation in the political process is essential for Iraq's passage to democracy.
Parliament has until August . 15 to draft a new constitution, which will be put to a referendum two months later.
If ratified, it will be the basis for a general election in December, giving Iraq its first, full-term elected government in decades.