In the statement a man identified himself as Salah Abou Mohammad, a spokesman for the group.
The blast left a crater three metres wide, wrecked the outside of the building and damaged nearby homes, shops and a cafe.
The attack was the first since two bombs exploded on December 11 in Algiers, killing at least 37 people.
Al-Qaeda in the Islamic Maghreb claimed responsibility for those attacks.
String of attacks
The same group had claimed responsibility for several other bombings.
In September 2007, a car bomb killed 37 people at a coastguard barracks in Dellys, 100km east of Algiers.
The attack happened two days after a suicide bomb blast targeting a convoy carrying Abdulaziz Bouteflika, Algeria's president, killed 22 people.
Al-Qaeda in the Islamic Maghreb was formed from the Salafist Group for Preaching and Combat (GSPC) in January 2007, with leader Abu Musab Abdel Wadoud promising to wage a violent campaign.
The GSPC was formed in 1998 by former members of Algeria's Armed Islamic Group which began attacking the government in 1992 after it cancelled elections an Islamic party looked set to win.
More than 150,000 people died in the ensuing decade-long civil war.