CNN affiliate BFM-TV reported that a French nurse who was working on the site at the time of the attack was freed.
Former hostage Stephen McFaul had plastic explosives strapped around his neck, duct tape over his mouth and rope around his hands, his brother Brian McFaul told CNN from Belfast.
McFaul made a break for freedom after the vehicle he was in -- one of several targeted by Algerian fighters -- crashed, with the explosives still around his neck.
"The joy was unreal," Brian McFaul said upon hearing his brother was safe. "I haven't seen my mother move as fast in all my life, and my mother smile as much, hugging each other ... You couldn't describe the feeling."
Americans were among the hostages at the In Amenas facility in Algeria, White House spokesman Jay Carney said without specifying how many. There could be as few as three American hostages, two U.S. officials said Wednesday.
One of the kidnapped Americans is a Texas man, a family member told CNN.
By Thursday night, some Americans had been freed and had spoken with relatives back home, while others remained unaccounted for, U.S. officials said.
"This incident will be resolved -- we hope -- with a minimum loss of life," said U.S. Secretary of State Hillary Clinton. "But when you deal with these relentless terrorists, life is not in any way precious to them."
The man behind the group claiming responsibility for the attack and kidnappings is a veteran jihadist known for seizing hostages.
Moktar Belmoktar, an Algerian who lost an eye fighting in Afghanistan in his teens, has long been a target of French counterterrorism forces. Libyan sources said he spent several months in Libya in 2011, exploring cooperation with local jihadist groups and securing weapons.
Two oil companies that operated at the site -- BP and Statoil -- said they were pulling non-essential personnel from Algeria.
"Our focus is 100 percent on the safety and welfare of those people and their families, and we are now beginning a staged and planned reduction in non-essential workforce on a temporary basis, pulling them out of the country," said BP Vice President Peter Maher from London.
The militants said they carried out the operation because Algeria allowed French forces to use its air space in attacking Islamist militants in Mali. Media in the region reported that the attackers issued a statement demanding an end to "brutal aggression on our people in Mali" and cited "blatant intervention of the French crusader forces in Mali."
U.S. Defense Secretary Leon Panetta, in Europe meeting with NATO allies, called the hostage-taking "a terrorist act."
Japan and the United Kingdom sent officials to Algeria. French President Francois Hollande earlier confirmed the presence of French citizens on the site but would not say whether any were hostages.
Cameron -- who canceled a planned Friday speech in the Netherlands -- talked Thursday with U.S. President Barack Obama about the situation, according to a Downing Street statement.
Before Algeria launched its military operation, U.S. officials had urged the Algerians to be cautious and make the hostages' safety their first priority, an Obama administration official said.
Algerian government officials did not warn their U.S. counterparts about the raid, the official said.
A senior U.S. official said U.S. officials did not trust the information they were getting from the Algerians, "because we hear one thing and then we hear something else."
Though there was concern that the Algerians' tactics may have put hostages in jeopardy, the official acknowledged they could have hit even harder.
"In all fairness, they could have ended it today," the senior U.S. official said. "They haven't used all the severeness they could. They know hostages are left."