Al-Qaeda's chief in Iraq says recent US air strikes have killed a militant wanted by Saudi Arabia, according to a statement on an Islamist website.
Rashud reportedly died during the US offensive in western Iraq
Abu Musab al-Zarqawi purportedly said Abdullah al-Rashud was killed in a US military operation in Qaim, a restive city close to the Syrian border.
Rashud is one of three people still at large on Saudi Arabia's list of 26 most wanted militants.
The authenticity of the web statement could not be verified.
Around 1,000 US and Iraqi soldiers took part in Operation Spear last week to root out rebels and foreign fighters in Anbar province, western Iraq, near the Syrian border.
Ground troops were backed up by air power, with some of the fiercest fighting taking place in the towns of Karabila and Qaim.
Some 50 rebels were killed and another 100 captured, the US military said at the time.
"Let the Islamic nation rejoice with the martyrdom of Abdullah al-Rashud," said the statement.
It said 37-year-old Rashud had gone to Iraq about six months earlier to join the insurgency against US and Iraqi forces.
Rashud was said to be one of al-Qaeda's main ideologues in the country.
He was number 24 on Saudi Arabia's most wanted list.
Jordanian-born Zarqawi is the most wanted suspect in Iraq and has a US bounty of $25m on his head.
His group has claimed responsibility for many of the biggest attacks of the insurgency.