Despite reports from Algerian state news agency APS that the crisis had ended last night, the FCO in London said in a statement that it was "on-going".
At least one British national has been killed and Prime Minister David Cameron has said the country "should be prepared for bad news".
Many Britons are currently unaccounted for. Scots are known to have been among the hostages held. At least one is thought to have escaped unhurt.
A Foreign Office spokesman said: "The terrorist incident in Algeria remains ongoing. The Prime Minister spoke twice to his Algerian counterpart, prime minister Abdelmalek Sellal, on Thursday.
"He chaired Cobra twice on Thursday, and will chair another meeting on Friday morning; Cobra will continue to meet as long as the crisis lasts.
"As the Prime Minister and Foreign Secretary have said, to the best of our knowledge on the information given to us by the Algerian government, one British national has sadly been killed.
"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.
"Our priority will remain the safety of British nationals and their co-workers. We cannot provide any details that might endanger their lives. But we are working round-the-clock to resolve this crisis."
Mr Cameron will chair a meeting of the Cobra emergency committee this morning as efforts continue to establish the full scale of the bloodshed.
Foreign Secretary William Hague has cut short a visit to Australia to return to the UK and there is expected to be a ministerial statement to the Commons.
The Algerian rescue effort was launched early yesterday morning without consultation with the UK, to the dismay of Number 10.
Mr Cameron was informed that it was under way when he telephoned his Algerian counterpart yesterday morning despite having earlier asked to be kept fully updated.
Offers of British help had been declined.
There was jubilation for one family yesterday as father-of-two Stephen McFaul, 36, from west Belfast, made contact with his wife Angela to say he was safe and well.
The Irishman fled after the vehicle he had been travelling in crashed after coming under attack from Algerian forces. He was able to run off and make it to safety.
His 13-year-old son Dylan choked back tears as he declared he would give the electrician a "big hug" as soon as he sees him and never let him go overseas again.
"I am very happy, I just cannot wait for him to come home," he said.
Mr McFaul's sister Donna McBride said: "We are absolutely delighted that he is free and is unharmed.
"I feel so sorry for the rest of the families who have lost loved ones and others who are missing."
She said her brother was currently with officials in Algeria in a debriefing exercise.
The Belfast man made contact with his family at around 3pm yesterday, Ireland's Department of Foreign Affairs said.
The married man said he was "safe and well" and was no longer a hostage.
Mr McFaul's father Christopher said his son was an easy-going, happy-go-lucky person who took everything in his stride, but that he was worried for him and delighted that he had come through the ordeal at the gasfield complex in Amenas.
"I never doubted it but it is hard to say in those situations," he said.
Mr Cameron cancelled his long-awaited Europe speech which he had been due to deliver in the Netherlands today after a second call to Algerian premier Abdelmalek Sellal.
Downing Street said Mr Cameron had "emphasised the continuing need for the Algeria security forces to do everything they could to safeguard hostages".
Speaking afterwards, he said: "We should be prepared for the possibility of further bad news, very difficult news, in this extremely difficult situation."
Officials would continue "working around the clock to do everything we can to keep in contact with the families, to build the fullest possible picture of the information and the intelligence".
"I will do everything I can to update people about what is a difficult and dangerous and potentially very bad situation," he added.
The militant group believed to have carried out the raid on the gas plant said it was retaliation for French military intervention against al Qaida-backed rebels in neighbouring Mali.
The drama began on Wednesday morning when heavily-armed militants launched a dawn raid, killing two people and injuring six others.
They claimed to have seized 41 foreign workers including Britons, Americans, Norwegians and Japanese.
A spokesman for the militants claimed that 35 hostages and 15 rebels had been killed when Algerian helicopters strafed the site in today's operation.
The militants - reportedly led by the veteran jihadist Mokhtar Belmokhtar - threatened previously to "eliminate" the hostages if they were attacked.
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