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As the hostage situation entered its fourth day, a senior Algerian government official said there were no talks planned with the militants.

"They are being told to surrender, that's it," the official said on the third day of the crisis. "No negotiations. That is a doctrine with us."

The United States said for the first time that Americans were among the remaining captives and confirmed the first known death of an American hostage, Frederick Buttaccio, 58, of Katy, Tex. Linked In, the social networking site for professionals, lists a Frederick Buttaccio as a sales operations coordinator for BP, the British energy giant that helped run the complex, but a company official said it would not comment on any employee who may have been at the facility.

The French foreign minister, Laurent Fabius, said one French citizen, Yann Desjeux, had been killed, but that "the lives of three others of our compatriots who were on the site during the terrorist attack have been saved." And the Norwegian energy firm Statoil said that while two employees had been brought to safety, six other workers for the company, all of them Norwegian nationals, were unaccounted for.

French television Saturday that shooting had erupted again at the site early Saturday, but gave no details..

All foreign governments with citizens at risk were still scrambling for basic information about the missing as they ferried escaped hostages out of the country on military aircraft and urged Algeria to use restraint.

"This is an extremely difficult and dangerous situation," Secretary of State Hillary Rodham Clinton told reporters in Washington. Describing a conversation she had earlier Friday with Algeria's prime minister, Abdelmalek Sellal, Mrs. Clinton said she had emphasized to him that "the utmost care must be taken to preserve innocent life."

Algeria's state news agency, APS, said 12 Algerian and foreign workers had been killed since Algerian special forces began an assault against the kidnappers on Thursday. It was the highest civilian death toll Algerian officials that have provided in the aftermath of the assault, which freed captives and killed kidnappers but also left some hostages dead in one of the worst mass abductions of foreign workers in years.

Previous unofficial estimates of the foreign casualties have ranged from 4 to 35. The American who died, Mr. Buttaccio, lived in a gated community in Katy, a suburb that is about 30 miles west of downtown Houston.The Algerian news agency also said that 18 militants had been killed and that the country's special forces were dealing with remnants of a "terrorist group" that was still holding hostages in the refinery area of the gas field in remote eastern Algeria.

It also gave a new sense of how many people may have been at the facility when the militants seized it on Wednesday, asserting that nearly 650 had managed to leave the site since then, including 573 Algerians and nearly half of the 132 foreigners it said had been abducted. But that still left many people unaccounted for.

The senior Algerian official, who spoke on condition of anonymity, said he believed there were about 10 hostages, under the control of possibly 13 to 15 militants, but he emphasized that "nothing is certain" about the numbers, which have varied wildly since the crisis began. He also said that there were other workers on the site "who are still in hiding" but that the Algerian military had secured the residential part of the gas-field complex.

"What remains are a few terrorists, holding a few hostages, who have taken refuge in the gas factory," he said. "It's a site that's very tricky to handle."

The official also challenged the criticism made in some foreign capitals that the Algerian military had acted hastily and with excessive force. On the contrary, he said, Algerian forces had returned fire only as the militants sought to escape the complex with their captives.

"There was a reaction by the army," he said. "They tried to flee and they were stopped," the official said of the militants. "They came absolutely to blow the whole site up. These are bitter-enders."

Earlier Friday, the State Department spokeswoman, Victoria Nuland, said that not all Americans had been freed. "We have American hostages," she said, offering the first update on what was known about United States citizens since officials confirmed on Thursday that seven or eight of them had been inside the gas-field complex.

Ms. Nuland also said the United States would not consider a reported offer made by the kidnappers to exchange two Americans for two prominent figures imprisoned in the United States — Omar Abdel Rahman, a sheik convicted of plotting to bomb New York landmarks, and Aafia Siddiqui, a Pakistani woman convicted of shooting two American soldiers in Afghanistan. It was impossible to confirm that offer, which was reported by the Washington-based SITE Intelligence Group, a service that tracks jihadist activity on the Internet.

Intensifying the uncertainties, a spokesman for the militants, who belong to a group called Al Mulathameen, said Friday that they planned further attacks in Algeria, according to a report by the Mauritanian news agency ANI, which maintains frequent contact with militant groups in the region. The spokesman called upon Algerians to "keep away from the installations of foreign companies because we will suddenly attack where no one would expect it," ANI reported.

The Algerian military operation to end the gas-field siege was done without consulting foreign governments whose citizens worked at the facility. It has been marked by a fog of conflicting reports, compounded by the remoteness of the facility, near a town called In Amenas that is hundreds of miles across the desert from the Algerian capital, Algiers, and close to the Libyan border.

In London, Prime Minister David Cameron told Parliament that the number of Britons at risk was estimated late Thursday at "less than 30." That number has now been "quite significantly reduced," he said, adding that he could not give details because the crisis was continuing. British officials have said they know at least one Briton was killed when the militants seized the facility.

Offering a broad account of Algeria's handling of the operation, he told lawmakers: "We were not informed of this in advance. I was told by the Algerian prime minister while it was taking place. He said that the terrorists had tried to flee, that they judged there to be an immediate threat to the lives of the hostages and had felt obliged to respond."

In Paris, Foreign Minister Laurent Fabius confirmed for the first time that a French citizen had been killed, although it was not clear exactly when. The victim, whom Mr. Fabius identified as Yann Desjeux, had contacted relatives as recently as noon Thursday, according to the French newspaper Sud Ouest, which also said it had spoken with Mr. Desjeux. Three other French citizens were involved in the hostage situation but are now safe, Mr. Fabius said.

Frustration with Algeria's information vacuum seemed particularly vexing to Japan, where an energy company that had assigned 17 employees to the gas-field facility said Friday that seven were confirmed safe but that 10 were unaccounted for. Prime Minister Shinzo Abe had personally appealed to his Algerian counterpart by phone early Friday to stop the military action, the Asahi Shimbun newspaper reported, but was told that military action was "the best response and we are continuing our operation."

Defense Secretary Leon E. Panetta met with Mr. Cameron in London as Pentagon officials were continuing to try to learn details about the raid.

"We are working around the clock to ensure the safe return of our citizens, and we will continue to be in close consultation with the Algerian government," Mr. Panetta said in a speech in London before meeting with Mr. Cameron.

A separate hostage situation of sorts appeared to have been averted at a village in Mali, the neighboring country where a French military intervention to stop radical Islamists may have been the catalyst for the Algerian gas-field seizure by the Al Mulathameen group. But details were sketchy.

A senior French official in Paris said Malian Islamist fighters, threatened by French and Malian soldiers, had occupied the village, Diabaly, and were threatening to use residents as human shields if attacked. But by Friday evening, a local official in Diabaly said the Islamists and most of the villagers had fled. "There's practically nothing left in Diabaly except burned-out vehicles and boxes of ammunition," said the official, Benco Ba, a local parliamentary deputy.

The Algerian fighters had been prepared to attack the gas complex for nearly two months, the militants' spokesman said, according to the ANI report, because they believed that the Algerian government "was surely going to be the ally of France" in the Malian conflict.

Hostages and analysts have said the attackers appeared well-prepared and deeply knowledgeable about the site, and there was evidence to suggest they had informers on the site or were in contact with workers there. An official at BP indicated earlier in the week that the attackers had shut off production at the site at the time of the attack, for instance. And at least two former hostages, interviewed independently, have said the fighters were aware of labor tensions and plans for a strike among catering workers on the site.

"We know you're oppressed; we've come here so that you can have your rights," the militants told Algerians on the site, according to one former hostage. Another hostage said the fighters had asked about the plans for a strike.