Al Jazeera quoted the speaker as saying: "We, Al-Qaeda Organisation in the Islamic Maghreb, claim responsibility for the bombing of the bus of the Russians, who fight Islam and its followers and our brothers in Chechnya.
"We ask the Muslim Algerian people, to keep away from the infidels and tyrant posts to avoid future attacks."
Website confirmation
The attacks were also verified in a statement posted on an Islamic fighter group website.
"Our fighters conducted an attack on the municipal guard in Tizi Ouzou and killed a number of infidels," the web statement said.
An Algerian newspaper had reported that armed men suspected of belonging to Islamic groups killed seven policemen in an ambush in Tizi Ouzou east of the capital Algiers.
The newspaper added that the fighters had detonated an explosive device at two cars carrying police officers and then opened fire on them, killing five and wounded another three, two of whom died in hospital.
The police managed to kill two of the policemen.
Breakout of violence
The group, previously known as the Salafist Group for Preaching and Combat, or GSPC, threatened in an earlier Internet statement to target Algerian soldiers.
Last month it claimed to have carried out seven simultaneous bombings on February 13 in Algeria that killed six people.
Violence broke out in Algeria in 1992 after the military-backed authorities, fearing an Iran-style revolution, scrapped a parliamentary election that an Islamic political party, the Islamic Salvation Front (FIS), was set to win.
Up to 200,000 people were killed in the ensuing bloodshed.
Attacks by armed fighters have fallen sharply in recent years but guerrilla raids by re-grouped Islamic fighters and shoot-outs with government forces persist, mainly in the Boumerdes and Tizi Ouzou regions to the east of Algiers.