The attack, it said, meant to "wreck the bastions of infidelity" of what it describes as the pro-Iranian government of Prime Minister Nouri al-Maliki.
The statement listed targets al-Qaida claimed to have hit, including the finance, foreign and defense ministries in central Baghdad. The statement, posted on a Web site commonly used by terror groups, could not be independently verified.
The wave of explosions that ripped through Baghdad last Wednesday - with nearly simultaneous truck bombs hitting Iraq's Foreign and Finance ministries - killed at least 101 people and left more than 400 wounded. It was the deadliest day of coordinated bombings since Feb. 1, 2008, when two suicide bombers killed 109 people at pet markets in Baghdad.
The U.S. military said the attacks bore the hallmarks of al-Qaida, which is known for its high-profile vehicle bombs and simultaneous suicide attacks.
The al-Qaida statement Tuesday said it sought to kill Iraqi government officials. It said the explosions "shook the earth under their feet and tore apart their hearts of fear and horror, proving to everyone the weakness of their government."
But it also expressed regret "for those innocent people who were killed" because they were accidentally at the targeted sites and wished the wounded speedy recovery. It warned of more attacks, and urged people to "keep away from the places" of the "heretic" Iraqi establishment.
Al-Maliki has blamed Sunni insurgents linked to al-Qaida in Iraq, a group that is part of the Islamic State in Iraq, for the attacks and has said security measures must be reassessed.
The prime ministers and other Shiite politicians also linked Saddam Hussein loyalists to the explosions. Such allegations are not new, and hard-line Shiite politicians have been increasingly mentioning the Baathists as partners with al-Qaida.
However, a branch of Saddam's former Baath party, now based in Syria, issued a statement denouncing the attacks.
Al-Qaida signature attacks until now have mostly seemed designed to fuel sectarian tensions and push the country back to the Sunni-Shiite violence of 2006 and 2007 that nearly led to civil war.
Wednesday's bombings differed because they hit symbols of state authority and appeared aimed at having a far-reaching political impact, further undermining the government and casting fresh doubt on the ability of Iraqi security forces following the departure of U.S. forces from major cities on June 30.