Algeria's prime minister says 37 foreign hostages were killed during the four-day gas plant crisis - with several executed with a bullet to the head.
Abdelmalek Sellal said at least one Canadian was among the gang of kidnappers also from Egypt, Mali, Niger, Mauritania and Tunisia and that the kidnappers crossed the border from northern Mali before swooping on the desert installation.
He said that 29 of the militants were killed and three arrested as the siege was brought to an end by an Algerian military assault at the weekend.
The update came as Prime Minister David Cameron addressed parliament on the hostage crisis - saying Britain's top priority was to bring home the bodies of the victims.
Mr Cameron spoke about the growing terror threat in North Africa, which he said is becoming a "magnet for jihadists" who share a "poisonous ideology".
Mr Sellal said one Algerian hostage was also killed - bringing the total hostage death toll to 38 - and that at least five foreigners are still missing.
The hostage-takers' leader Mohamed el-Amine Bencheneb, an Algerian militant known to the country's security services, was killed during the army assault, Mr Sellal said.
Three Britons are now known to have died and three more are believed to be dead. A UK resident from Colombia is also thought to have died.
Mr Cameron told the House of Commons there should be a "strong security response" and "intelligent political response" to tackle the "murderous violence" seen in Algeria.
"We must frustrate the terrorists with our security beat them militarily address the poisonous narrative they feed on; close down the ungoverned space in which they thrive; and deal with the grievances they use to garner support," he said.
Veteran terrorist Mokhtar Belmokhtar's Mulathameen Brigade has threatened to carry out more attacks unless Western powers cease operations in neighbouring Mali, according to a Mauritanian news agency.
In a statement the al Qaeda-linked group, whose name means "The Masked Ones", reportedly said the hostage-takers offered negotiations on freeing the gas plant captives but that Algerian authorities responded with a military assault.
A Downing Street spokesman has ruled out the possibility of Britain sending troops into combat to support France's intervention against Islamist rebels in neighbouring Mali.
Three of the Britons killed have been named as Kenneth Whiteside, 59, from Glenrothes, Paul Morgan, 46 and Garry Barlow, 49, both from Liverpool.
The brother of Mr Whiteside, Bob, told Sky News his family first heard of his death from Facebook.
An Algerian colleague, who witnessed the killing, had posted a farewell message to Mr Whiteside, calling him a "smiler".
Later, the colleague described to the family how he was shot in the head by the terrorists along with four other hostages.
"He did say Kenny was smiling the whole way through. He'd accepted his fate by this time. It's a terrible the way he died but it's typical of the world we live in today. It's a horrible place," said his brother.
Mr Morgan was reported to be a former Foreign Legion soldier and Gulf War veteran who was in charge of security at the In Amenas plant.
His mother Marianne, 65, and partner Emma Steele, 36, described him in a statement as a "true gentleman".
They said: "Paul was a true gentleman, a family man, he very much loved his partner Emma, his mum, brothers and sister, of whom he was very proud.
"He loved life and lived it to the full. He was a professional man proud to do the job he did and died doing the job he loved.
"We are so proud of him and so proud of what he achieved in his life. We are devastated by Paul's death and he will be truly missed."
Married father-of-two Mr Barlow was a system supervisor for BP at the In Amenas plant.
In a statement released through the Foreign Office, his widow Lorraine said: "Garry was a loving, devoted family man. He loved life and lived it to the full.
"He was very much loved by myself, his sons, mother and sister and the rest of his family and friends and will be greatly missed.
"He was very proud of his family, as they were of him. We are totally devastated by the news of his death."
The siege ended on Saturday and Algerian authorities warned the figure of 23 hostages killed at the remote facility would rise sharply.
Bomb squads searching for booby-trap devices left by the Islamist militants discovered 25 bodies, some so badly disfigured they could not be identified.
A Filipino survivor of the siege has told how foreign hostages were used as human shields to prevent Algerian troops firing on them from helicopters.
Father-of-four Joseph Balmaceda said: "Whenever government troops tried to use a helicopter to shoot at the enemy, we were used as human shields.
"We were told to raise our hands. The government forces could not shoot at them as long as we were held hostage."
Mokhtar Belmokhtar sent a video to a Mauritanian-based news website in which he claimed one of his cells, known as "Those Who Sign In Blood", was responsible for the attack.
Foreign Secretary William Hague branded the militants "cold-blooded murderers" and said reports they had "executed" seven of their hostages before the final battle could well be true.