"The operation against UN headquarters ... is the result of information gathered by the intelligence services of Muhammad's Army," the group said in a 10-minute video aired on Lebanon's LBC1 channel on Saturday.
In the video statement, which showed seven hooded and armed figures, the group hinted that Tuesday's bombing, which killed 23 people, including the top UN envoy to Iraq, Sergio Vieira de Mello, and injured more than 100, was aimed at US intelligence agents present in the UN headquarters at the time.
It also demanded US forces leave Iraq or face "lesson after lesson."
The men were notably dressed in the uniforms of Saddam Hussein's Fedayeen, a militia loyal to the ousted Iraqi leader, and were carrying rocket-propelled grenade launchers and other weapons.
The UN attack had already been claimed on Thursday by another group calling itself the Armed Vanguards of Muhammad's Second Army, in a video aired on the Dubai-based al-Arabiya satellite channel.
Muhammad's Army had previously surfaced on 9 August when gunmen claiming association with a variety of unknown factions, including that one, appeared in a video aired on al-Arabiya and vowed more attacks on the US-led occupation force.
However, in that video they also condemned a huge car bomb attack outside the Jordanian embassy in Baghdad two days before, saying it was the work of "traitors."
Some 150 Shia Muslims demonstrated outside the ruins of the UN headquarters on Saturday, condemning the devastating attack on the world body's offices and offering their condolences.
March organiser Sadeq Al-Timimi (R) expresses Iraqis' regret
"All Iraqis were saddened after the attack but before coming, we waited for the condemnation by Ali al-Sistani (a top Shia religious authority in Iraq) whose heart is bleeding because of what happened," organiser Sadeq al-Timimi, 39, told a UN official who received representatives of the group.
Al-Sistani sent a message of condolences to UN Secretary General Kofi Annan on Friday over the death of de Mello and others killed in the blast.
"The Iraqi people condemn the terrorist attack on the UN building in Baghdad," said a banner held up by the demonstrators, who held a minute's silence to pay tribute to those killed in the truck bomb blast.
"We came here independently of all parties," said Timimi, who was one of 10 demonstrators permitted to enter the secured area at the UN premises.