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The operation on Thursday was reported to have freed captives, killed kidnappers but left some hostages dead. Foreign leaders scrambled to find out the fates of their citizens.

Almost a day after the raid, there was no official word on Friday on the number of hostages who had been freed, killed or still held captive. Estimates of the foreign casualties ranged from 4 to 35, though one Algerian official said the higher figure was "exaggerated."

In London on Friday, British officials said the Algerian authorities had not informed them that the military operation deep in the desert near the border with Libya had been concluded. Until the British heard otherwise, one official said, speaking in return for anonymity, "we are working on the basis that it's an ongoing operation."

The official declined to comment on widespread reports that British authorities were bracing for high casualty figures among up to 20 Britons thought to have been working at the installation. French officials said on Friday that there had been "very few" French nationals at the site and at least two of them were safe.

The British Foreign Office said: "We are not in a position to give further information at this time. But the Prime Minister has advised we should be prepared for bad news." It remained unclear whether the British assessment meant that the Algerian military was confronting or pursuing kidnappers or whether the hostage takers were believed to be still holding captives.

Algeria's reported silence about the situation on the ground seemed to deepen frustration among foreign governments with citizens who had worked at the plant, close to the Libyan border.

On Thursday, despite requests for communication and pleas to consider the safety of their abducted citizens, the United States, Britain and Japan said they had not been told in advance about the military assault, stirring frustration that the Algerians might have been overly aggressive and caused needless casualties.

But the Algerian government, which has a history of violent suppression of Islamist militancy, stood by its decision to deal forcefully with the kidnappers, who were holding Algerians and citizens of nine other countries.

"Those who think we will negotiate with terrorists are delusional," the communications minister, Mohand Saïd Oublaïd, said in an announcement about the assault on the facility near In Amenas, in eastern Algeria, close to the Libya border. "Those who think we will surrender to their blackmail are delusional."

The midday assault came more than 24 hours after a militant group, which the Algerians said had ties to jihadis in the region, ambushed a bus carrying gas-field workers to a nearby airport and then seized the compound. It was one of the boldest abductions of foreign workers in years.

The abductions were meant to avenge France's armed intervention in neighboring Mali, Mr. Oublaïd said, a conflict that has escalated since French warplanes began striking Islamist fighters who have carved out a vast haven there.

On Thursday, the United States became more deeply involved in the war, working with the French to determine how to best deploy American C-5 cargo planes to ferry French troops and equipment into Mali, according to an American military official.

The United States has long been wary about stepping more directly into the Mali conflict, worried that it could provoke precisely the kind of anti-Western attack that took place in Algeria, with deadly consequences. After the raid to free the hostages, the Algerians acknowledged a price had been paid.

"The operation resulted in the neutralization of a large number of terrorists and the liberation of a considerable number of hostages," said Mr. Oublaïd, the communications minister. "Unfortunately, we deplore also the death of some, as well as some who were wounded."

Algerian national radio described a scene of pandemonium and high alert at the public hospital in the town of In Amenas, where wounded hostages and those who escaped were sent. The director of the hospital, Dr. Shahir Moneir, said in the report that wounded foreign hostages were transferred to the capital, Algiers.

In a telephone interview from the hospital, an Algerian who escaped, who identified himself as Mohamed Elias, said some of the hostages had exploited the chaos created by the Algerian assault to flee. "We used the opportunity," he said, "and we just escaped."

Senior American military officials said that aides traveling in London with Defense Secretary Leon E. Panetta were struggling to get basic information about the raid, and that an unarmed American Predator drone was monitoring the gas-field site.

One senior official said that possibly seven to eight Americans were among the hostages — the first official indication of the number of Americans involved — and that he did not know if any had been killed in the raid.

Prime Minister David Cameron of Britain said his office had not been told ahead of time, an implicit criticism of the Algerian government. A spokesman said that Mr. Cameron had learned of the raid through Britain's own intelligence sources and that "the Algerians are aware that we would have preferred to have been consulted in advance."

Mr. Cameron told reporters the situation was "very dangerous" as he and other British officials gathered for the third time Friday for a meeting of the government's COBRA crisis committee.

The gravity of the situation prompted him to take the unusual step of canceling plans to deliver a major speech in Amsterdam in which he had planned to warn European Union leaders to undertake reforms or see Britons "drift toward the exit."

Japan also expressed strong concern, saying Algeria had failed not only to advise of the operation ahead of time, but to heed its request to halt the operation because it was endangering the hostages.

"We asked Algeria to put human lives first and asked Algeria to strictly refrain," the chief cabinet secretary, Yoshihide Suga, quoted Prime Minister Shinzo Abe as telling his Algerian counterpart, Abdelmalek Sellal, by telephone late Thursday.

The situation is "very confused," President François Hollande of France said at a news conference in Paris and was "evolving hour by hour." Mr. Hollande gave the first official confirmation that French citizens were among the captives.

A European diplomat who was involved in the effort to coordinate a Western response to the hostage seizure said that the information available to the United States, France and Britain had been "confusing at best, and sometimes contradictory."

Several Western officials complained that the Algerians appeared to have taken none of the usual care exercised to minimize casualties when trying to free hostages.

"They care deeply about their sovereign rights," said the European diplomat, who spoke on the condition of anonymity because of the matter's delicacy.

Even before reports of the Algerian military's raid began to emerge, many hostages — Algerian and foreign — were reported to have escaped as the kidnappers failed to persuade the Algerian authorities to give them safe passage with their captives.

The Algerian news site T.S.A. quoted a local official, Sidi Knaoui, as saying that 10 foreigners and 40 Algerians had managed to flee after the kidnappers made several attempts to leave with the hostages.

Ireland confirmed that an Irish citizen, Stephen McFaul, had escaped. The man had contacted his family and was "understood to be safe and well and no longer a hostage," Irish officials said.

Earlier, a French TV station, France 24, quoted an unidentified hostage as saying the attackers "threatened to blow up the gas field."

Algeria's interior minister, Daho Ould Kablia, said the seizure of the gas field had been overseen by Mokhtar Belmokhtar, an Algerian who fought in Afghanistan in the 1980s and had reportedly established his own group in the Sahara after falling out with other Qaeda leaders.

The description of the leader was one of the most specific pieces of information given by the Algerians on a day of vague and contradictory accounts of the abduction and raid. Well into the night, officials warned that hostages were still being held inside the compound and that the crisis remained unresolved.

"It's a painful situation. It's not over," said a senior Algerian official. "I can't tell you how many are left in there. No numbers. None at all. Nothing is certain."