The blast on Saturday killed at least five people and wounded a senior Interior Ministry official.
"Your brothers in the Jama'at al-Tawhid and Jihad attacked the treacherous apostate the Deputy Interior Minister General Abd al-Jabar in front of his home as he was preparing to go to his office," said the statement carried on an Islamist website.
The blast damaged the home of Abd Al-Jabar Yusuf, located about 200 metres from the headquarters of the former Iraqi general security service.
More than an hour after the blast, Iraqi police were still picking up body parts and putting them in plastic bags for burial. Five cars were burnt out, two of them upside down.
Thick black smoke could be seen pouring into the air and half a dozen cars were ablaze after the bomb detonated just before 0400 GMT, as residents were leaving homes in the area to go to work.
Yusuf, one of three deputy interior ministers and a member of the Shia Dawa party, is reported to be in a stable condition.
On Monday, a car bombing killed the president of the Iraqi Governing Council, Izz al-Din Salim and about six other people near the headquarters of the US-run occupation authorities in the capital.
Clashes have been ongoing in
Najaf for several weeks
Meanwhile, violent clashes have erupted between US occupation forces and members of Shia leader, Muqtada al-Sadr's Mahdi army in the vicinity of the 1920 revolution square in Najaf city, Aljazeera's correspondent in Iraq reported on Saturday.
Mortar bombs, rocket-propelled grenades and machineguns have been used during the clashes, injuring four Iraqis, the correspondent said.
Rocket-propelled grenades have been also fired at the grand market and al-Rafidain bank in the city, causing extensive damage, the correspondent added.
Meanwhile, a car bomb has killed a US soldier and wounded three others in an attack south of Baghdad, the US occupation army said on Saturday.
The military said the soldiers were patrolling near the town of Mahmudiya, 30km south of Baghdad, when their vehicle was hit by a "vehicle-born improvised explosive device". They did not say when the attack occurred.