Communications Minister Mohand Said Oublaid said in a statement broadcast on national radio the military action was still ongoing, The New York Times reported.
"The operation resulted in the neutralization of a large number of terrorists and the liberation of a considerable number of hostages," Oublaid said. "Unfortunately, we deplore also the death of some, as well as some who were wounded. We do not have final numbers."
Oublaid said the government attempted to negotiate a peaceful end to the drama.
"But confronted with the determination of the heavily armed terrorist group, our armed forces were forced to surround the site and fire warning shots," he said. "In front of the stubborn refusal of these terrorists to heed these warnings and confronted with their evident desire to leave Algeria with the foreign hostages to then use them as a bargaining chip, an assault was launched this Thursday at the end of the morning."
Unconfirmed reports earlier in the day indicated 35 hostages and 15 kidnappers had died in the attack, the Times said. ABC News reported five of the 10 Americans being held had been freed, but the fate of the others was unclear.
The British and French foreign ministries, along with the Algerian government, confirmed the Algerian army assault on the BP natural gas facility in Amenas, seized Wednesday by militants to protest of French involvement in fighting in Mali.
Secretary of State Hillary Clinton said U.S. counter-terrorism experts have been in close contact with their Algerian counterparts.
"Now, let me say, the situation is very fluid. It's in a remote area of Algeria, near the Libyan border," Clinton said during a press availability with the president of Somalia. "The security of our Americans who are held hostage is our highest priority, but of course we care deeply about the other Algerian and foreign hostages as well."
State-run Algerian news agency APS said four foreign hostages and 600 Algerian hostages had been freed by the Algerian army.
Mauritania's ANI news agency reported seven hostages -- three Belgians, two Americans, one Japanese and one British citizen -- were still being held.
A British government source described the figures reported by ANI as "high," The Guardian said.
The standoff started when militants identifying themselves the Battalion of Blood, which has ties to al-Qaida, stormed the plant, demanding a halt to a French military operation against al-Qaida-linked Islamic militants in Mali.
Algerian Interior Minister Daho Ould Kablia said the hostage-takers were led by Mokhtar Belmokhtar, a Islamic guerrilla who fought in Afghanistan in the 1980s and later established his own following in Africa after having a falling out with other local al-Qaida leaders, The Guardian said.
The militants reportedly threatened to blow up the gas facility at Amenas, near the Libyan border, if government commandos attempted to free the hostages, several media outlets reported.
France 24 television reported a male hostage said in a telephone interview attackers forced some hostages to strap on suicide belts. Whether the man was a hostage could not be confirmed.
Hundreds of Algerian soldiers surrounded the facility and helicopters flew overhead, the Los Angeles Times said. Algerian officials earlier said they would not negotiate with the militants, who sought safe passage to Libya.
Algerian officials said two people were killed in Wednesday's assault, which began with an ambush on a bus taking workers to an airport.
U.S. Defense Secretary Leon Panetta, in Europe for a NATO meeting, told ABC News Thursday the situation was a "terrorist attack."
"I want to assure the American people that the United States will take all necessary and proper steps that are required to deal with this situation," Panetta said.
More than 100 Algerian nationals also were held captive but released Wednesday, the Interior Ministry said.
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