Islamists with the Masked Brigade, who have been speaking through a Mauritanian news outlet, said the Algerians opened fire as the militants tried to leave the vast Ain Amenas energy complex with their hostages a day after seizing the installation deep in the desert.
Algerian forces had surrounded the complex in a tense standoff since the plant was seized early Wednesday and had vowed not to negotiate with the kidnappers, who reportedly were seeking safe passage.
President Barack Obama's government offered military assistance Wednesday to help rescue the hostages, but the Algerian government refused, a U.S. official said in Washington. He spoke on condition of anonymity because he was not authorized to speak publicly about the offer.
Information about the 41 foreign hostages the militants claimed to have — including seven Americans — was scarce and conflicting. All were reportedly workers at the remote plant.
The spokesman for the Masked Brigade said Thursday the surviving hostages included three Belgians, two Americans, a Briton and a Japanese citizen. The information from the militants came from the Nouakchott Information Agency, which has often carried reports from al-Qaida-linked extremist groups in North Africa.
Ireland said an Irish hostage had made contact with his family and was safe and free.
Algeria's national news service, however, said four hostages were freed during the military operation Thursday, citing a local law enforcement source. An Algerian security official had said earlier that 20 foreign hostages had escaped before the raid.
There was no way to verify the information independently and the Algerian government did not immediately comment on the hostages or the military operation.
The Norwegian energy company Statoil had said 12 of its employees had been captured by the militants — nine Norwegians and three locals — while Japanese media reported at least 3 Japanese among the hostages and Malaysia confirmed two.
Japanese and British authorities, as well as BP — which jointly operates the complex with other energy companies — said they had been told by the Algerians there was an ongoing operation Thursday to free the hostages.
Algerian state radio reported earlier Thursday that 30 local workers managed to escape from the plant, but hundreds of Algerian workers had already been released Wednesday by the hostage-takers.
The kidnapping is one of the largest ever attempted by a militant group in North Africa, and the militants phoned a Mauritanian news outlet to demand that France end its intervention in neighboring Mali to ensure the safety of the hostages.
After the initial militant attack, Algerian troops surrounded the isolated gas plant, located 800 miles (1,300 kilometers) south of the capital of Algiers.
Algerian Interior Minister Daho Ould dismissed theories that the militants had come from Libya, 60 miles (100 kilometers) away, or from Mali, more than 600 miles (1,000 kilometers) away. He said the roughly 20 well armed gunmen were from Algeria itself, operating under orders from Moktar Belmoktar, al-Qaida's strongman in the Sahara.
Yves Bonnet, the former head of France's spy service, also dismissed the idea that the operation was specifically linked to the French action in Mali due to the amount of organization it involved.
"It was an operation conceived well in advance — spectacular and needing a lot of preparation ... It was not at all an improvised operation," he told the Europe 1 radio. "The operation was probably already scheduled and simply getting all those people into the desert would take several days."
It is certainly the largest haul of hostages since 2003, when the radical group that later evolved into al-Qaida in North Africa snatched 32 Western tourists in Algeria. This is also the first time Americans have been involved.
BP, the Norwegian company Statoil and the Algerian state oil company Sonatrach, operate the gas field. A Japanese company, JGC Corp, provides services for the facility as well.
British Foreign Secretary William Hague told BBC radio he had dispatched a team to Algeria to help at the British embassy there.
"Excuses being used by terrorists and murderers who are involved — there is no excuse for such behavior, whatever excuse they may claim," he said. "It is absolutely unacceptable, of course. It is, in this case, the cold-blooded murder of people going about their business. So there is no excuse, whether it be connected to Libya, Mali or anywhere else."
U.S. Defense Secretary Leon Panetta had declared Wednesday that the U.S. "will take all necessary and proper steps" to deal with the plant attack, condemning it as "terrorist attack."
Associated Press writers Kimberly Dozier in Washington, Lori Hinnant in Paris