The Algerian military operation to free hostages being held by Islamist militants at a desert gas plant is now over, state news agency APS reports.
State TV said four foreign hostages were killed in the operation. Others were freed, but there was no confirmation of how many survived.
AFP news agency quoted officials as saying the army had not secured the whole site, which was being searched.
Al-Qaeda-linked fighters occupied the facility near In Amenas on Wednesday.
Reports suggest the facility is still being searched.
During the Algerian military intervention on Thursday as many as 600 Algerians and four foreign hostages – two from Scotland, one from France and one from Kenya – were freed, APS reported.
The Irish government confirmed that one of its citizens was free. Five American hostages had survived and had left the country, US officials were quoted as telling ABC News.
The Algerian military operation to free hostages being held by Islamist militants at a desert gas plant is now over
Earlier, the militants reportedly said that at least 34 hostages and 14 kidnappers died, and that seven foreign hostages had survived.
They had claimed to be holding 41 foreign nationals, believed to include British, Japanese, US and Norwegian citizens, in retaliation for French military intervention in neighboring Mali.
Some workers were reported to have been freed or to have escaped before the Algerian raid.
Algerian Communications Minister Mohamed Said Belaid said a “significant number of terrorists” were killed during the raid.
He added: “Unfortunately, we deplore some deaths and some people wounded. We don’t yet have the numbers.”
Details of how the raid unfolded were slow to emerge.
APS reported that the Algerian military, which had been surrounding the gas plant, had targeted two vehicles as they tried to escape from the site with an unknown number of people on board.
Militants told local media that Algerian forces had opened fire from the air.
Norwegian Prime Minister Jens Stoltenberg said he was told by his Algerian counterpart that Algerian authorities had tried and failed to find a solution to the stand-off on Wednesday night. “The Algerian prime minister said they felt they had no choice but to go in,” he said.
British Prime Minister David Cameron was informed that the raid was under way when he called the Algerian Prime Minister at 11.30 GMT, a spokesman said.
David Cameron, who cancelled a key speech on Europe scheduled for Friday, made it clear that he would have preferred to have been told in advance, the spokesman added.
Japan’s government protested against the raid, urging Algeria “put the highest priority on people’s lives”. The US said it was “seeking clarity” on what had happened.
Algerian Interior Minister Daho Ould Kablia said the kidnappers were Algerian and operating under orders from Mokhtar Belmokhtar, a senior commander of al-Qaeda in the Islamic Maghreb (AQIM) until late last year.
Daho Ould Kablia said they had entered Algeria from Libya, AFP reported.
Two people were killed when militants attacked the gas plant.
The Tigantourine gas facility is about 40 km (25 miles) south-west of In Amenas, which is close to the Libyan border and about 1,300km (800 miles) south-east of Algiers.
BP operates the gas field jointly with Algerian state oil company Sonatrach and Norwegian firm Statoil.
Algerian troops have surrounded a gas facility in the east of the country where foreign workers are being held hostage by Islamist militants.
The kidnappers occupied the complex at In Amenas on Wednesday, after killing a Briton and an Algerian in an attack on a bus.
Algeria says some 20 foreign nationals are being held hostage, although the kidnappers say they have 41.
The captives include British, Japanese, US, French and Norwegian nationals.
One statement purported to be from the hostage-takers demanded an end to the French military intervention against Islamist rebels in Mali.
Algerian Interior Minister Daho Ould Kabila said the militants wanted to leave the country with the hostages, but he had refused to let them go.
“We reject all negotiations with the group,” he told reporters late on Wednesday.
Daho Ould Kabila added that the kidnappers were Algerian and operating under orders from Mokhtar Belmokhtar, a senior commander of al-Qaeda in the Islamic Maghreb (AQIM) before late last year, when he set up his own armed group after apparently falling out with other leaders.
Minister Daho Ould Kabila said a heavily armed “terrorist group” had attacked a bus carrying workers from In Amenas at about 05:00 on Wednesday.
The gas field is operated by the Algerian state oil company, Sonatrach, along with the British oil company BP and Norway’s Statoil.
It is located about 1,300 km (800 miles) south-east of Algiers, and about 60 km (37 miles) west of the Libyan border.
The attackers were repelled by police who had been escorting the bus, but a Briton and an Algerian national had been killed, Daho Ould Kabila said.
Two other British nationals, a Norwegian, two police officers and a security guard were also hurt in the fire fight, he added.
Afterwards, the militants drove to the gas facility’s living quarters and took a number of Algerian and foreign workers hostage.
Dozens of Algerian workers were later released.
Senior al-Qaeda commander Mokhtar Belmokhtar has been identified as the leader behind Algeria kidnapping
The foreign nationals were being held in one wing of the living quarters, which the security services and army had surrounded, Daho Ould Kabila said.
“Since then, they’ve been facing off. The security forces are consolidating their position around the base,” he added.
Early on Thursday, British Foreign Secretary William Hague confirmed that a Briton had died and that “a number” of others were being held hostage.
He described the killings as the “cold-blooded murder of people going about their business”.
A worker told France’s Le Figaro newspaper the captors had mined the facility and demanded food, water and vehicles.
Daho Ould Kabila said nearby border crossings had been closed as a precaution and that the foreign ministry was in contact with diplomats from the hostages’ countries.
UK Foreign Secretary William Hague confirmed the captives included “a number of British nationals”, adding: “This is therefore a very dangerous situation.”
He said the UK government was working “around the clock” to resolve the crisis.
US Secretary of Defence Leon Panetta said he could not confirm the exact number of Americans seized in the attack.
“By all indications this is a terrorist act and the United States strongly condemns these kinds of terrorist acts,” he said.
Meanwhile Norwegian Prime Minister Jens Stoltenberg said 13 Norwegian employees of Statoil were believed held hostage at the gas facility. Irish Foreign Minister Eamon Gilmore said one of its nationals was a hostage.
Japanese news agencies, citing unnamed government officials, said there were three Japanese hostages.
Two groups led by Belmokhtar – the Khaled Abu al-Abbas Brigade and the Signed-in-Blood Battalion – said they were behind the incident.
Earlier, a man claiming to be a spokesman for the militants said al-Qaeda had carried out the attack.
A list of demands had been sent to Algerian authorities, and the hostages would be killed if troops attempted to rescue them, the spokesman added.
”Storming the gas complex would be easy for the Algerian military, but the outcome of such an operation would be disastrous,” he warned.
In a statement carried on Mauritanian media, the Signed-in-Blood Battalion said it would hold the Algerian and French governments and the nations of the hostages responsible if its demands were not met, saying they must bring an end to the French intervention in Mali.
Militant groups have vowed to avenge the intervention, where French forces have been battling Islamists linked to AQIM for the past week.
Algeria has been allowing French aircraft to use its air space.
Fought Soviet forces in Afghanistan in late 1980s
Former leading figure in al-Qaeda in the Land of the Islamic Maghreb. Left in late 2012 after falling out with leaders
Now heads the Khaled Abu al-Abbas Brigade and the Signed-in-Blood Battalion
Known as “The One-Eyed” as he wears an eyepatch over a lost eye
French intelligence has dubbed him “The Uncatchable”, while locals refer to him as “Mister Marlboro” for his illicit cigarettes operation