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Two coalition aircraft struck the building with "laser-guided munitions" at around 5:30 am (0130 GMT), US Central Command said in a statement.
"A full assessment of the strikes effectiveness is in progress," it said.
Basra has been surrounded by British troops for nearly two weeks.
Majid ordered the 1988 mustard gas attack on Halabja village to suppress a Kurdish uprising backed by Iran, which was at war with Iraq. An estimated 5,000 people died, most of them women and children.
Considered a right-hand man of Saddam, Majid was put in charge of defending southern Iraq ahead of the US-led war launched March 20 to topple Saddam's regime.
"Ali is a member of the Iraqi president's inner circle and holds the military title, 'southern commander of forces'," the Central Command statement said.
A British army source said the residence was targeted on information that Ali was present.
"He was seen entering a building by a reliable source on the ground," he said.
"The building was subsequently targeted and hit by both air strikes and artillery. There is a strong chance that anyone caught inside would have been killed or seriously injured."
New York-based Human Rights Watch in a report earlier this year called for the arrest and prosecution of Majid, saying he was responsible for the deaths or "disappearances" of around 100,000 non-combatant Kurds when he put down their revolt.
Al-Majid held authority over state agencies in Iraq's Kurdish regions at the end of the 1980-88 Iran-Iraq war.
He later played key roles in Iraq's 1990-91 occupation of Kuwait and in the suppression of a Shiite Muslim uprising in the wake of the first Gulf war.
SPACE.WIRE |