STORY HIGHLIGHTS
- NEW: U.S. State Department identifies three citizens killed in the Algeria gas plant standoff
- Britain's prime minister praises Algerian forces that ended the standoff
- At least 37 hostages died in terrorist attack and raid on gas complex, Algeria says
- The attackers came from northern Mali, an Algerian official says
(CNN) -- At least 37 hostages died in the terrorist seizure of, and ensuing special forces assault on, a natural gas plant in Algeria, the country's prime minister said Monday.
Five other hostages are missing from the In Amenas complex and could be dead, Prime Minister Abdul Malek Sallal said.
Before Sallal's statement Monday, other countries and companies that employed foreign workers at the sprawling plant had confirmed a total of 29 hostage deaths.
Among the dead were three Americans, State Department spokesman Victoria Nuland said Monday. She identified them as Victor Lynn Lovelady, Gordon Lee Rowan, and Frederick Buttaccio, who had been previously identified.
The Algerian state-run news service APS said 29 militants also died in the standoff, which ended Saturday after four days when Algerian special forces stormed the complex for the second time to free hostages. The government said it did so because the militants were planning to blow up the installation and flee to neighboring Mali with hostages.
"If it exploded, it could have killed and destroyed anything within 5 kilometers or further," Sallal said.
The plant employed 790 people, including 134 foreign workers, Sallal said Monday.
Read more: Bloody Algeria hostage crisis ends after 'final' assault, officials say
The crisis began Wednesday when militants in pickup trucks struck a sprawling natural gas complex in In Amenas, gathered the Westerners who worked there into a group and tied them up.
After taking control of the facility, the well-armed militants planted explosives throughout the complex, Sallal said.
The military tried to negotiate with the militants, but their demands to release militants held prisoner in Algeria were deemed unreasonable, leading to intervention by special forces troops backed by the Algerian Air Force, Sallal said.
Read more: Nations scramble to account for missing after Algeria hostage crisis
At one point, the militants tried to flee the compound in vehicles that carried explosives and three or four hostages as human shields, Sallal said. At least two of the vehicles flipped and exploded during the attempt, he said.
The attack involved months of planning and involved militants from eight countries -- Algeria, Tunisia, Egypt, Mali, Niger, Canada and Mauritania, according to APS.
Sallal said the terrorist team that took the hostages had entered the country from northern Mali, where Malian and French authorities are battling Islamists who control the area.
One-eyed veteran Islamist fighter Mokhtar Belmokhtar has claimed responsibility for the hostage-taking on behalf of his al Qaeda-linked group, according to Mauritania's Sahara Media news agency.
He said it was in retaliation for Algeria allowing France to use its airspace to battle Islamist militants in Mali. But regional analysts believe the operation was too sophisticated to have been planned so quickly.
The plant in eastern Algeria is run by the state oil company, in cooperation with foreign firms such as Norway's Statoil and Britain's BP -- and as such, employed workers from several foreign countries.
Read more: Algerian forces seek 'peaceful' settlement of dramatic, deadly hostage crisis
British Prime Minister David Cameron said Monday that the international effort to evacuate workers is complete and that offcials are turning their attention to gaining access to the plant and returning the bodies of the slain British hostages to Great Britain.
Cameron also praised Algerian forces for their work in ending the crisis, and said they have no responsibility for the deaths that occurred as forces tried to regain control of the plant.
"This would have been a most demanding task for security forces anywhere in the world, and we should acknowledge the resolve shown by the Algerians in undertaking it," Cameron said. "Above all, the responsibility for these deaths lies squarely with the terrorists."
Here is the latest breakdown on the international hostages:
Colombia
Colombia's president said a citizen was presumed dead.
France
No known French hostages are unaccounted for, the defense ministry said.
A man identified as Yann Desjeux died after telling French newspaper Sud Ouest that he and 34 other hostages were treated well. It was unclear what led to his death.
Japan
Ten Japanese remain unaccounted for, according to JGC, a Yokohama-based engineering firm. Japan is sending a second team that includes doctors to the scene of the standoff. Other government officials have been at the site since last week.
Malaysia
Three hostages were on their way back home, state media reported. There is a "worrying possibility" that another is dead while a fifth is unaccounted for, the agency said.
Read more: Algeria attack may have link to Libya camps
Norway
Five Norwegians are missing, while eight are safe, according to the Norwegian Prime Minister.
Philippines
Six Filipinos are confirmed dead and four are missing, the nation's foreign affairs ministry said. In addition, 16 Filipinos are accounted for and confirmed alive, according to a ministry spokesman.
Romania
One Romanian lost his life while four others were freed, the country's foreign ministry said.
United Kingdom
Three British citizens were killed, the Foreign Office said Sunday. Three other British nationals and a UK resident are also "believed dead," according to British officials. The Foreign Office confirmed the name of one of the slain hostages, Garry Barlow, in a statement Monday.
"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," the Foreign Office quoted his wife, Lorraine, as saying.
Twenty-two other Britons who were taken hostage have safely returned home.
United States
While three Americans died, seven U.S. citizens survived the attack, Nuland said Tuesday. Beyond identifying the dead, she declined further comment, citing privacy considerations.
Read more: Algeria attack may have link to Libya camps
CNN's Yoko Wakatsuki contributed to this report.