The Mulathameen Brigade that claimed the mass hostage-taking in Algeria threatened to carry out more attacks unless Western powers ended what it called an assault on Muslims in neighboring Mali, according to the SITE monitoring service.
In a statement on Monday, the al-Qaida linked group also said the hostage-takers had offered negotiations on freeing the captives seized at a gas plant deep in the Sahara but the Algerian authorities used military force, SITE reported.
The statement was published by the Mauritania-based Nouakchott News Agency, according to SITE, which tracks statements by militants.
The group said it would attempt further such attacks if there was no halt to Western military involvement in northern Mali, which militant groups call Azawad and where French forces are fighting to end control by Islamist groups.
"We promise all the countries that participated in the Crusader campaign against the Azawad region that we will carry out more operations if they do not reverse their decision," the statement said.
The hostage death toll from the four-day siege at the gas plant has risen to almost 60.
Algerian Prime Minister Abdelmalek Sellal is expected to give details on Monday about one of the worst international hostage crises in decades, in which American, British, French, Japanese, Norwegian and Romanian workers were killed or are missing.
The fighters seized the base on Wednesday, capturing a plant that produces 10 percent of Algeria's natural gas exports, and a residential barracks nearby. They demanded an end to French air strikes against Islamist fighters in Mali that had begun five days earlier.
Governments express misgivings about Algerian reaction
"We opened the door for negotiations with the Westerners and the Algerians, and granted them safety from the beginning of the operation, but one of the senior (Algerian) intelligence officials confirmed to us in a phone call that they will destroy the place with everyone in it," SITE quoted the statement as saying.
The siege turned bloody on Thursday when the Algerian army opened fire saying fighters were trying to escape with their prisoners. Survivors said Algerian forces fired at several trucks in a convoy carrying both hostages and their captors.
The Brigade said that at one point the gunmen decided to move the hostages to a factory on the site, SITE said.
"The helicopters bombed the convoy that was moving the hostages to the factory and destroyed it including everyone inside, in a barbaric and direct method of killing.
"This indicates the army's indifference to preserving the lives of the detained, as it claims."
The statement said its fighters continued to offer negotiations. "The Algerian army did not respond to these legitimate demands; rather, they started storming the gas factory, which led to the killing of the hostages."
Western leaders have said responsibility for the deaths lies with the hostage-takers. Nevertheless, some governments whose nationals were taken captive have expressed misgivings about the incident, in particular about Algeria's apparent decision to proceed with military action without informing them beforehand.
Veteran jihadist Mokhtar Belmokhtar claimed responsibility for the hostage-taking by his Mulathameen Brigade - whose name means "The Masked Ones" - in the name of al-Qaida, in a video cited by the Mauritanian news website Sahara Media on Sunday.
He said about 40 attackers took part in the raid, roughly matching the government's figures for fighters killed or captured.