In a statement on a website, the Ansar al-Sunna group said "two of our martyr brothers attacked the two dens of Satan in Arbil" on Sunday.
"Our joy on Eid al-Adha was boosted by this attack against the agents of Jews and Christians," the statement said.
At least 105 people were killed in the blasts set off by two men strapped with explosives at the offices of two prominent Kurdish political parties in Arbil, some 330km north of Baghdad.
The Ansar al-Sunna also expressed sympathies with the "brothers" of the group Ansar al-Islam, blamed by the Kurdish Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK) for the attacks.
The blasts wrecked the offices of the two parties and killed many of their senior members.
"Our joy on Eid al-Adha was boosted by this attack against the agents of Jews and Christians"
Meanwhile, Iraqi police defused a bomb placed near the car of the pro-US Iraqi Governing Council member Ahmad Chalabi in the northern city of Mosul.
The explosive device was discovered and defused before dawn, a police spokesman said.
Elsewhere, a city council member in the restive Iraqi town of Fallujah and his nephew were wounded by gunmen who sprayed their car with gunfire.
Sheikh Hisham al-Alussi was returning home with his nephew Muhammad Taghlob, when they were attacked. Alussi was seriously wounded.
US occupation forces claimed they had arrested nine men suspected of planning attacks on northern oil facilities and companies.
Officials said three former Iraqi intelligence officers were among those arrested.