"We are dealing with men who think according to their indoctrination. They obey blindly. They cannot be reasoned with," Interior Minister Abderahmane Meziane Cherif said in Algiers.
In a recent interview in the Algerian Arabic-language daily newspaper Essalam, one unidentified GIA leader was quoted as describing foreigners as ''the main coronary artery" of a plan to "colonize" the country with non-Muslim unbelievers.
"Killing and fighting them is the practical message to weaken the unbeliever rulers," he said.
In some GIA propaganda, the group claims to be the heir of the first wave of Muslim guerrilla activists in Algeria. This movement was considered to have been knocked out of action after its founder, Mustapha Bouyali, was killed in 1986 by security forces.
His followers were arrested and sentenced to death, but were freed early in 1990 under pressure from the emerging Islamic Salvation Front (FIS). The FIS, now outlawed, is the country's main Muslim fundamentalist political force.
The GIA imposed as a key qualification for its leaders that they take part directly in violent operations. "They should experience armed operations and must demonstrate that they have killed significant numbers among God's enemies," the leader said.
The last GIA chief was Cherif Gousmi, 26, known as Abou Abdallah, who was killed in a gun battle with security forces near Algiers in September. The GIA's No. 3, Abdessalam Djemaoune, was gunned down alongside Gousmi.
According to Algeria's official APS news agency, Djemaoune was known as the group's specialist in slitting throats - including those of 12 Croatian Christians killed at a foreign workers' camp a year ago.
Gousmi had headed the group since February when its former chief, Mourad Sid Ahmen, alias Djaraf al-Afghani, was killed with nine of his men in a gun battle in an Algiers suburb. Security forces said they had found a letter with Gousmi's body from Ali Belhadj, No. 2 in the FIS political command, urging Muslim rebels to intensify their war against the army-backed government.
But beyond that reported link with Belhadj, political analysts are baffled about the relationship between the GIA and the FIS, which has its own armed wing called the Salvation Islamic Army.
Some say the groups represent two faces of the same coin, while others see them as competitors.
Algerian newspapers reported in November that the newly appointed GIA leader, Abou Abderrahmane Amine, was seeking cooperation with the FIS to confront a buildup of security forces launched earlier that month after talks between President Liamine Zeroual and FIS leaders collapsed.