The Foreign Office said the Algerian authorities confirmed that an operation was under way at the gas plant deep in the desert at In Amenas where the hostages were being held.
Reuters reported a local source as saying that six hostages and eight of their captors were killed in an Algerian strike on the complex close to the Libyan border.
The militants contacted a news agency in neighbouring Mauritania to claim that 35 hostages and 15 militants died when Algerian helicopters began strafing the plant.
Seven hostages remain alive - including one Briton, two Americans, three Belgians, and one Japanese - the militants said.
Amid conflicting reports, an Algerian official said earlier today that 20 people, including Europeans and Americans, had managed to escape the kidnappers.
An Irishman caught up in the Algerian hostage crisis has been freed.
Stephen McFaul, 36, from west Belfast, made contact with his family at around 3pm, Ireland's Department of Foreign Affairs said.
The married man said he was "safe and well" and was no longer a hostage.
Fears had been growing for the safety of Mr McFaul as conflicting and contradictory reports emerged about the ongoing terrorist incident at the In Amenas gas field complex in the east of the African country.
The Belfast man had managed to contact his relatives twice before while in captivity.
But after receiving no further contact since yesterday, his family made a plea for him to be released unharmed, earlier today.
In a statement, issued through local MP Paul Maskey, they said they were very concerned about his welfare.
But just two and a half hours later, he made contact with them to say he was free.
Downing Street has confirmed that Britain was not informed in advance of the Algerian decision to stage a military intervention in the hostage crisis.
David Cameron was told that an operation was under way only when he telephoned the Algerian prime minister at 11.30am today.
The Prime Minister made clear that he would have preferred to be informed in advance, but the Algerians said they had had to act "immediately".
"The Prime Minister is extremely concerned. It is a very grave and serious situation," the spokesman said.
Mr Cameron discussed the situation by telephone with US president Barack Obama and French president Francois Hollande.
The militant group believed to be holding the hostages has claimed that it carried out the attack in retaliation for the French military intervention against al Qaida-backed rebels in neighbouring Mali.
The Prime Minister was due to chair a second meeting today of the Whitehall emergency Cobra committee to discuss the latest developments.
The spokesman said: "Our thoughts are with all the hostages and their families and friends at an intensely difficult time."
The terrorist group claimed it targeted the Westerners, including seven Americans, in retaliation for the French military intervention against al Qaida-backed rebels in neighbouring Mali.
First Minister Alex Salmond told MSPs that a number of Scots are among those being held hostage.
The Foreign Office has declined to reveal the number of Scots held, but it is thought to be fewer than five.
Mr Salmond said at Holyrood: "I should tell the chamber that I spoke with the Prime Minister this morning about the hostage-taking situation in Algeria.
"As the chamber will know a terrorist group has seized the BP Statoil facility in the Algerian Sahara.
"Citizens of a number of nationalities are involved, including UK citizens. I can confirm to the chamber a number of Scots are among the hostages.
"The UK Government reports that one UK national has been killed in the attack. I know the chamber will understand in the interests of the safety and security of the hostages, the information that can be given out is necessarily limited.
"The priority is their safety and of course to keep the families informed. The Scottish police service is fully engaged with the Metropolitan Police on the latter and Scottish Government ministers are in contact with the Foreign and Commonwealth offices on the former.
"This is a hugely serious situation and I know that the whole chamber is united, both in condemnation of the attack, and also in hoping for the early and safe release of the hostages."
David Cameron's spokesman said the situation was "very serious and dangerous" but the Government was "working through" the Algerians and BP, which part controls the facility that was stormed.
Mr Cameron made clear in a telephone call with his Algerian counterpart last night that Britain would consider "any requests that they make for assistance", his spokesman said. However, none had been made so far.
Asked whether the Government was happy with the co-operation being offered by the Algerian government, he said: "We are in close contact with them and it's very important that we continue to be so."
A Government source said: "This is a situation where the Algerian government, understandably, very much sees itself as in the lead in its sovereign territory."
BP said armed groups were still on-site holding a number of its staff, and described the situation as "unresolved and fragile".
The family of a 36-year-old married Irishman, from west Belfast, who has been taken hostage have appealed for his release.
In a statement read by Sinn Fein MP Paul Maskey, they said they have not heard from him since the compound was attacked.
They said: "We are all very concerned about his welfare and want to see him released to us as a matter of urgency, free from harm. Our thoughts are with him and all the other captives."
A second meeting of the Government's emergency response committee Cobra was held this morning and another will be convened this afternoon.
Arrangements are in place for Mr Cameron to chair a further Cobra meeting from The Hague tomorrow morning, when he will be in the Netherlands to deliver his long-awaited speech on Britain's relationship with the European Union.
The ANI news agency in neighbouring Mauritania quoted a source from the alleged hostage-takers as saying that Algerian army helicopters had begun to attack the complex.
The source from the group calling itself "Signatures in Blood" said two Japanese hostages were injured in the assault.
The militants threatened to "eliminate" the hostages if the Algerians tried to storm the plant.
The Algerian security official said those who escaped included Americans and Europeans. He did not give any further details.
Militants attacked the Ain Amenas gas complex 800 miles (1,300 kms) south of Algiers yesterday, taking dozens of foreign workers hostage. Those being held included Japanese, Britons, French, Americans, Malaysians and Norwegians, among others.
The gas plant has been surrounded by the Algerian army and there is now a tense stand-off with the militants.
Some 30 Algerian workers fled the complex earlier in the day, suggesting that the militants are having trouble managing the many hostages they have taken at the vast natural gas complex, the third largest in oil-rich Algeria.
Algerian authorities, meanwhile, were talking with tribal Algerian Tuareg leaders in hopes of mediating the dispute.
The group claiming responsibility - called Katibat Moulathamine or the Masked Brigade - originally said it had captured 41 foreigners, including seven Americans.
Two people, one a Briton and the other Algerian, were killed in the initial assault, which the US defence secretary has called "a terrorist attack." The kidnapping is one of the largest ever attempted by a militant group in North Africa.
The hostage-takers are reportedly seeking a safe passage out of the isolated area, something Algerian authorities have already rejected.
Another Algerian official said authorities are in contact with tribal elders among Algerian Tuaregs, who are ethnically related to the rebels fighting the Mali government, some of whom have close al Qaida links.
The France-based head of a catering company at the plant told French media before the latest escape that some 40 foreigners appeared to be held hostage in a separate area from the Algerian workers.
Regis Arnoux of the Mareseille-based CIS Catering company said while electricity to the plant has been cut, it had at least three weeks of food supplies.
Militants phoned a Mauritanian news outlet to say one of its affiliates had carried out the operation and that France should end its intervention in Mali to ensure the safety of the hostages.
But the militants themselves appeared to have no escape, cut off by surrounding troops and army helicopters overhead. Algerian Interior Minister Daho Ould Kabila said it appeared that the militants were hoping to negotiate their departure away from the area - a notion he rejected.
"Security forces have surrounded the area and cornered the terrorists, who are in one wing of the complex's living quarters," Mr Kabila said.
He also rejected theories that the militants had come from Libya, 60 miles away, or from Mali, more than 600 miles away. He said the roughly 20 well armed gunmen were from Algeria itself, operating under orders from Moktar Belmoktar, al-Qaida's strongman in the Sahara.
Yves Bonnet, the former head of France's spy service, also dismissed the idea that the operation was specifically linked to the French action in Mali due to the amount of organisation it involved.
"It was an operation conceived well in advance - spectacular and needing a lot of preparation ... It was not at all an improvised operation," he told the Europe 1 radio. "The operation was probably already scheduled and simply getting all those people into the desert would take several days."
BP, the Norwegian company Statoil and the Algerian state oil company Sonatrach, operate the gas field. A Japanese company, JGC Corp, provides services for the facility as well.
It was not immediately possible to confirm the identities of the hostages. Ireland said a 36-year-old Irish man was among them, and Britain and the US said their citizens were taken, without giving numbers. The Norwegian company Statoil said 12 of its employees were captured - nine Norwegians and three locals. Japanese media reported at least 3 Japanese among the hostages and the Malaysian government confirmed two of its citizens were taken.
In Rome yesterday, US Defence Secretary Leon Panetta declared that the US "will take all necessary and proper steps" to deal with the attack in Algeria. He would not detail what such steps might be but condemned the action as "terrorist attack."
BP said it would not identify staff members who were taken hostage for security reasons. "BP's overriding priority is to do all we can to ensure the safety of our staff and to support their families during this anguishing time," BP CEO Bob Dudley said in a statement.