The suicide car bombings were the first major attacks in Algiers since the 1990s civil war.
Prime Minister Abdelaziz Belkhadem, who was not harmed, called the attack a "cowardly, criminal terrorist act" while speaking to reporters outside the damaged building.
"This criminal attack is perpetrated at the time when the Algerian people are seeking national reconciliation,'' Belkhadem said, according to Bloomberg news.
The attacks came after weeks of gun battles in Algeria's coastal mountains between security forces and Algeria's largest Islamic guerrilla group, which is allied to al-Qaida.
The group recently changed its name from the Salafist Group for Preaching and Combat to reflect its affiliation with Osama bin Laden's network. The group claimed responsibility for the bombings, along with attacks in neighboring Morocco, in an Internet statement.
Oil-rich Algeria has seen a resurgence of Islamic militant activity after several years of relative peace. The government offered amnesty to any Islamists who surrendered last year in an effort to prevent attacks.
In 1992, violence erupted in Algeria after authorities stopped a parliamentary election, which an Islamist political party was predicted to win. Around 200,000 people were killed in the resulting battles.
"For a while, it seemed that the authorities in (these) countries had broken the back of the Islamist terrorist networks," Magnus Ranstorp, a specialist at Sweden's national defense college, told the Agence France-Presse. "But it looks that these fronts have been re-energized, revitalized, perhaps because of the severity of the crackdowns."
French Foreign Minister Philippe Douste-Blazy voiced his "horror" over Wednesday's attacks. "I convey my sincerest condolences to the victims' families and assure the Algerian authorities of our full solidarity in their fight against terrorism," Douste-Blazy said in a statement.
In Morocco on Wednesday, police hunted possible suicide bombers in Casablanca, a day after three suspected militants blew themselves up.
