In a statement the group said there had been six bombs and claimed that more than 140 people had been killed or injured.
The statement said: "... the Mujahedeen [holy warriors] heroes successfully carried out a blessed conquest, where they detonated six car bombs concurrently targeting a number of police stations of the renegade pagans."
APS said two of the dead were police officers. It also reported 13 injured, and said 10 of them were police.
Police and hospital staff have reported more injuries than what the agency said.
In Boumerdes, doctor Said Lamri said by telephone that his hospital was treating 13 wounded.
Police said another 16 people were injured in Tizi Ouzou, 90km east of Algiers.
'Pools of blood'
Atiff Jumaa, a witness standing near the blast-pocked walls of Si Mustafa's police station, said the bomb went off early in the morning next to the building.
Pools of blood lay in the gutter of the main road, he said.
Residents said the police stations attacked were in Si Mustafa, Draa Benkheda, Meklaa and Zemouri villages.
Residents near Boumerdes said they were checking reports of a fifth bomb attack on a police station close to the town.
There were unconfirmed reports that the bombs were rigged in vehicles and set off remotely.
History of violence
Islamists began an armed revolt in 1992 after the then military-backed authorities, fearing an Iran-style revolution, scrapped a parliamentary election that an Islamist political party, the Islamic Salvation Front (FIS), was set to win.
Up to 200,000 people were killed in the ensuing bloodshed. The violence has sharply subsided in the past few years.
The Tizi Ouzou and Boumerdes districts are often the scene of clashes between Islamist fighters and security forces in the oil-and-gas-exporting North African country.
Tuesday's attacks were the first on police stations since near-simultaneous truck bombs exploded at two police stations on October 30, in the Algiers region, killing three people and wounding 24.
On December 10, a bomb exploded beside a bus carrying foreign oil workers in an up-market Algiers suburb, killing two people and wounding eight.
That attack was claimed in a video posted on the internet by the GSPC, the main rebel group fighting to install a purist Islamic rule.
A statement purporting to come from the GSPC and published in Algerian newspapers also claimed responsibility for the October 30 attacks.
The GSPC said last month it was adopting the name Al-Qaeda Organisation in the Islamic Maghreb.
Some security analysts believe the GSPC wants to transform itself from a domestic movement in Algeria, where it is under pressure from security forces, into an international fighting force capable of striking in both North Africa and Europe.