The Al-Qaeda-linked gunmen, cited by Mauritania's ANI news agency, said they still held seven foreigners at an Algerian gas plant deep in the Sahara desert near the border with Libya. An Algerian security official put their number at 10.
"This is an extremely difficult and dangerous situation," US Secretary of State Hillary Clinton said in Washington at a joint news conference with an equally concerned Japanese Foreign Minister Fumio Kishida.
"The United States extends our condolences to all the families who have lost loved ones in this brutal assault and we remain deeply concerned about those who remain in danger. Utmost care must be taken to preserve innocent life."
State Department spokeswoman Victoria Nuland identified the dead American as Frederick Buttaccio amid reports that a total of five Americans were initially taken hostage.
The UN Security Council "condemned in the strongest terms the terrorist attack in In Amenas, Algeria", said a statement agreed by the 15-member panel.
The council also expressed "deep sympathy and sincere condolences to the victims of these heinous acts and their families and to the people and governments of Algeria and those countries whose nationals have been affected".
International criticism of the haste with which Algeria launched a dramatic military assault to rescue those held has been mounting, after an Algerian security official said it had left dead 12 hostages and 18 kidnappers.
Kishida urged Algeria to place the "utmost priority" on ensuring the hostages' safety.
In Tokyo, Prime Minister Shinzo Abe ordered his government to do everything possible to ensure the safety of 10 Japanese nationals unaccounted for.
Abe attended a meeting of a government task force shortly after arriving in Tokyo after cutting short a trip to Southeast Asia.
"I would like you to do your best to confirm the safety of the Japanese and rescue them by using every possible means," Abe told top government officials at the meeting.
French Foreign Minister Laurent Fabius said a Frenchman had been killed in the operation. A US official said an American military transport plane had begun to help evacuate survivors, but gave no estimate of the number of US hostages.
Troops were trying to reach a "peaceful" end to the hostage crisis, before "neutralising the terrorist group that is holed up in the plant and freeing a group of hostages still being held there," a security official said.
The Al-Qaeda-linked gunmen group known as "Signatories in Blood" want an end to the French intervention in neighbouring Mali, according to Mauritania's ANI news agency, which quoted sources close to their leader, Mokhtar Belmokhtar.
The gunmen said they were still holding three Belgians, two Americans, one Japanese and a Briton, although Belgium said there was no indication that any of its nationals were being held.
ANI said Belmokhtar, a veteran Algerian extremist with Al-Qaeda ties who has claimed responsibility for the attack, also proposed exchanging the remaining two US hostages for the Egyptian blind sheikh Omar Abdul Rahman and Pakistani Aafia Siddiqui, jailed in the United States on charges of terrorist links.
"The United States does not negotiate with terrorists," Nuland said when asked about the proposal.
More workers remain unaccounted for, and the fate of at least 10 Japanese nationals and eight Norwegian hostages still unknown.
NBC News cited US officials as saying that two Americans escaped unscathed after hiding when the attack began, while the fate of two others remains unclear.
One American who escaped -- Mark Cobb -- told CNN via text message that he was "safe" after escaping with some Algerian staff.
Algerian news agency APS quoted a government official as saying the kidnappers, who claimed to have come from Niger, were heavily armed with machineguns, assault rifles, rocket launchers and missiles.
Clinton urged Algeria to show "utmost care" to preserve the lives of the hostages and offered condolences for those killed.
An AFP photographer saw trucks delivering empty coffins to the hospital at In Amenas, where the wounded had been taken.
US Defence Secretary Leon Panetta said the United States was "working around the clock" to secure the safe return of Americans, as Washington ruled out talks for a hostage swap.
Some of those who escaped said explosives had been wrapped around their necks and others said they hid, petrified, wherever they could.
Alexandre Berceaux of French catering firm CSI said he took cover in his room before troops freed him.
"I was under the bed and I put boards everywhere just in case," Berceaux said. "I had a bit of food, a bit to drink. I didn't know how long it would last."
The fate of two Malaysians believed to have been caught up in the hostage crisis remains unknown, the foreign ministry said in a statement Saturday.
Three other Malaysians who were working at the gas plant were safe. The embassy in Algeria "is still determining the fate" of the other two.
Philippine worker Jojo Balmaceda, employed by British oil giant BP, recounted on local television Saturday how he escaped from his kidnappers' clutches.
Balmaceda and three fellow Filipino workers were taken at gunpoint as they arrived for work, tied up and thrown into a truck along with Japanese and Malaysian hostages, the GMA network reported.
He escaped when the truck was hit by an explosion but sustained a gunshot wound to his head which had affected his hearing, the station added.
A Northern Ireland man, Stephen McFaul, also escaped. His brother said he fled when the convoy he was in came under army fire.
France said two of its nationals had returned safely but it had no word on two more. And Vienna said one Austrian had been released.
Algerian forces launched their rescue bid on Thursday, a day after the kidnappers seized the plant to avenge what they said was Algiers' support for French military action in neighbouring Mali.