ISI was reported to have said that the attack targeted "a group of Shias and 'apostates' who sold their faith for money and to be a tool in the war on Iraqi Sunnis".
The group also said that the security situation in the Iraqi capital was poor and could not stop its fighters.
Tuesday's attack occurred at the historical site of the country's defence ministry, a building that was turned into an army recruitment centre and military base after the 2003 US-led invasion.
Witnesses described the assailant as a blond young man who walked up to an officer and blew himself up.
On the day of the strike authorities indicated that al-Qaeda was behind the attack.
"The fingerprints of al-Qaeda are very clear in this attack," Major General Qassim Atta, a Baghdad security spokesman, said.
"You can see it in the timing, the circumstances, the target and the style of the attack - all the information indicates it was al-Qaeda behind this."
US troop reduction
The attack came a day after Iraqi legislators suspended talks on forming a new government.
The Iraqiya bloc headed by Iyad Allawi, Iraq's former prime minister, said on Monday that it had halted talks with the State of Law bloc headed by Nouri al-Maliki, the country's incumbent prime minister, in protest against al-Maliki's "sectarian tone".
Armed groups appear to be trying to take advantage of the power vacuum in Iraq, as politicians squabble over positions in a new government after an inconclusive March 7 election.
It also came two weeks ahead of a US deadline to cut its troop numbers to about 50,000, with troops in fact being drawn down by Thursday morning.
The last brigade left the country early Thursday, before the August 31 deadline for the end of Operation Iraqi Freedom pledged by Barack Obama, the US president, on taking office.
US troops will remain in the country in an advisory capacity, helping to train Iraqi forces in a new mission codenamed Operation New Dawn, which will run until the end of 2011.