In a statement posted on a militant website, the Islamic State of Iraq said it sent five men dressed in army uniforms and armed with weapons and explosive belts to attack the financial institution.
Photos posted on the same website showed the disfigured heads and body parts of men dressed in army fatigues buried among rubble of what al-Qaida said is the Central Bank.
Sunday's assault sparked clashes between militants and Iraqi security forces that lasted more than three hours and left more than 20 people dead.
It stoked fears that insurgents are taking advantage of political deadlock following March 7 elections to try to derail security gains as the U.S. prepares to withdraw its forces by the end of next year.
In the statement, the group called the strike "unique."
"The Bank was targeted because it is the artery that feeds the Satanic alliance with life via oil money and the stolen wealth of Muslims," said the statement.
It said that the militants took half an hour to take control of the Bank and destroy targets in the building before exchanging fire with guards and eventually blowing themselves up using explosive belts.
Also on Thursday, an anti-al-Qaida fighter and four family members were killed as they slept in their garden to escape the heat in a former insurgent stronghold west of Baghdad, officials said. It was the second attack against Sunni figures who have turned against the terror network in as many days.
Gunmen broke into the house of Khudr al-Issawi and opened fire on him and his family during the pre-dawn attack in a village near Fallujah, 40 miles (65 kilometers) west of Baghdad. The farmer, his wife, two daughters and a son were killed, according to local police chief Brig. Gen. Mahmoud al-Issawi. Another son was wounded.
The police chief, who blamed al-Qaida in Iraq, said the slain man was a member of one of the local government-backed Sunni militias known as Awakening Councils in the village of Fhelat. The groups helped changed the course of the war when they revolted against al-Qaida and joined the Americans in late 2006 and 2007.