Security forces said Muslim fundamentalists, fighting to overthrow the government, had planted the bomb that went off outside the central police station in Amirouche Street in the middle of the afternoon.
Omar Belhouchet, director of the El Watan newspaper, said that a suicide bomber had apparently driven the car bomb straight at the police station, according to a French radio report.
"The explosion took place just when the street was full of children, women and old people ... it is beyond barbarity," Algerian television said.
At the scene, bodies could be seen still burning and the street was deep in shards of glass from shattered windows.
Women were screaming as they searched for their children near the police station whose walls were blackened. All its windows were blown out.
A bus that was caught in the explosion as it came from Martyrs Square along the seafront was twisted and burnt along with a small car that is believed to have been carrying the bomb.
A witness, on the spot three minutes after the blast, said: "I saw policemen splashed with blood but I was not sure if it was their own blood or that of victims they were trying to save."
"I jumped through the window of the bus," said one woman, covered in blood.
The Interior Ministry ordered all doctors to report to Moustapha Hospital at the far end of the street, overlooking May First Square.
The shocked television announcer told viewers: "We have not shown you all the pictures, some are far too horrible."
The explosion took place less than 24 hours after the armed wing of Algeria's outlawed Islamic Salvation Front (FIS) told militants to increase their killings during the Muslim holy month of Ramadan which coincides with February.
The call to kill, reported in the Algerian Arab-language al-Hayat al Arabia on Sunday and made by the Islamic Salvation Army (AIS), added: "If the authorities are preoccupied today with the security situation, they should wait to see even more during this month, because the battle will be great."Reuse content