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French, British and American officials said the Algerian government had told them the military operation was over, but a senior Algerian government official said security forces were “doing cleanup” to make sure no kidnappers were hiding in the sprawling industrial complex. 

Western officials deplored the loss of life during the four-day siege, which Philip Hammond, the British defense secretary, called “appalling and unacceptable.” Defense Secretary Leon E. Panetta, who appeared with Mr. Hammond at a news conference in London, said he did not yet have reliable information about the fate of Americans at the facility, although the Algerian official said two had been found “safe and sound.” 

The provisional death toll released by Algeria Saturday, even by the government’s reckoning, was heavy. Out of dozens taken hostage on a site that employed hundreds of workers, 23 were dead while 32 kidnappers were killed, according to the government news service. That represents close to the initial estimate of hostage-takers. 

The government said it had recovered machine guns, rocket launchers, suicide belts and small arms. 

The Algerian news agency report did not give the nationalities of the hostages it said were executed Saturday, and it remained unclear whether there were other hostages at the remote plant and whether they were alive. Earlier news reports said at least 10 and as many as dozens of hostages from several nations were in the hands of the kidnappers as of Friday. 

United States officials had said that “seven or eight” Americans had been at the In Amenas field when it was seized by the militants on Wednesday. 

One American, Frederick Buttaccio, 58, of Katy, Tex., was confirmed dead on Friday, and the French government said one of its citizens, identified as Yann Desjeux, had also died before Saturday’s raid. Britain earlier said at least one of its citizens had been killed, and an Algerian state news agency said Algerians had also been killed as of Friday. 

The Algerian official, who would speak only on the condition of anonymity, said a precise tally would take time. 

“There are corpses that are totally charred,” he said. “We’ve got to do identification work. It’s very difficult.” Algerian officials have said some of the kidnappers blew themselves up. The Algerian news agency said the militants had set fire to part of the complex Friday night, which prompted the troops to launch the military assault Saturday. 

The raid, if it swept up all the attackers, would bring to an end a siege involving dozens of hostages and kidnappers that drew criticism from Western governments for the tough manner in which it was handled by the Algerian security services. Attacks on the kidnappers by the government forces caused an unknown number of deaths among the hostages, in addition to those who were executed by the militants, who may be linked to Al Qaeda. 

A militant who claimed responsibility for the attack, and who was blamed by the Algerians for leading it, Mokhtar Belmoktar, was until recently a leading commander of Al Qaeda’s North and West African branch, Al Qaeda in the Islamic Maghreb. 

One Algerian who managed to escape told France 24 television late Friday night that the kidnappers said, “We’ve come in the name of Islam, to teach the Americans what Islam is.” The haggard-looking man, interviewed at the airport in Algiers, said the kidnappers then immediately executed five hostages. The militants who attacked the plant said it was in retaliation for French troops sweeping into Mali this month to stop an advance of Islamist rebels south toward the capital. However the militants later said they had been planning an attack in Algeria for two months on the assumption that the West would intervene in Mali. 

The Algerian government has rejected the criticism of its go-it-alone approach, toughest from the British and Japanese governments whose nationals were among those kidnapped, saying they have had years of experience dealing with terrorist attacks. The Algerian government has also denied that it started the confrontation on Thursday, saying troops, who began their assault by firing on a convoy, were merely responding to the militants’ attempts to leave the field with hostages. 

The government official, however, acknowledged Saturday morning that the militant attack was of a scale and complexity the country had not experienced before. 

“This was a multinational operation,” he said of the kidnappers. “They’ve come from all over, Tunisia, Egypt, Mauritania. It’s the first time we’ve handled something on this scale. This one is different, it’s of another dimension,” he said. 

Nonetheless, the brazenness of the assault — dozens of fighters attacking one of the country’s most important gas-producing facilities — is likely to call into question Algeria’s much vaunted security strategy in dealing with the Islamic militants who shelter in its southern deserts, near the border with Mali. 

The Algerians have made a virtue out of keeping a lid on these militants, pushing them toward Mali in a strategy of modified containment, and ruthlessly stamping them out when they attempt an attack in the interior of the country. So far it has worked, and Algeria’s extensive oil and gas fields, extremely important revenue sources, have been protected. 

That relative success had allowed Algeria to take a hands-off approach to the Islamist conquest of northern Mali in recent months, even as Western governments pleaded with it to become more directly involved in confronting the militants, who move across the hazy border between the two countries. 

But now, with last week’s attack, Algeria may have to rethink its approach, analysts suggest, and engage in a more frontal strategy against the Islamists. 

The senior government official appeared to acknowledge this in the interview Saturday, saying: “This has international implications. This is not just about us, it’s international.” 

If the outcome represents a relative setback for Algeria, it could be viewed as a decided victory for the Islamists who carried out the assault on the gas plant, achieving several of their shared perennial goals: killing large numbers of Westerners and disrupting states they have put on their enemies list — including Algeria. 

Indeed, the militants said Friday they planned more attacks in Algeria, in a report carried on a Mauritanian news site that often carries their statements.