Islamist militants are believed to be still holding a number of hostages at a gas facility in the Algerian desert.
At least four foreign workers and several militants died on Thursday when troops stormed the living quarters.
The militants had claimed to be holding 41 foreigners. At least four were freed but the fate of many others is unknown.
Meanwhile, BP said hundreds of workers from international oil companies had been evacuated from Algeria on Thursday and that many more would follow.
Algeria has yet to give precise casualty figures from the rescue attempt.
The state-run APS news agency cited local officials as saying two Britons and two Filipinos were killed. Two others, a Briton and an Algerian, died on Wednesday when the militants ambushed a bus that was taking foreign workers at the facility to the local airport.
A spokesman for the militants told the Mauritanian ANI news agency that 35 hostages and 15 militants had been killed in Thursday's operation. One Algerian official said the figures were "exaggerated".
The In Amenas gas field is operated by the Algerian state oil company, Sonatrach, along with the British oil company BP and Norway's Statoil.
It is situated at Tigantourine, about 40km (25 miles) south-west of the town of In Amenas and 1,300km (800 miles) south-east of Algiers.
On Friday morning, the UK Foreign Office and Norwegian Foreign Minister Espen Barth Eide said they believed the incident was ongoing.
"Parts of the plant are under Algerian authorities' control, and other parts are not. This information is changing by the hour," Mr Eide told the BBC.
APS cited local officials as saying the military operation at the gas facility's living quarters, where most of the hostages were held, had ended on Thursday night.
"Hostages are still being held at the Tigantourine gas treatment plant, which is surrounded by special forces," APS added.
Later, UK Prime Minister David Cameron told Parliament that he had been told by his Algerian counterpart, Abdelmalek Sellal, that troops were "still pursuing terrorists and possibly some of the hostages".
"They are now looking at all possible routes to resolve this crisis," he added, describing the situation as "fluid and dangerous".
Mr Cameron also revealed that on Thursday night, the number of British citizens at risk had been fewer than 30, but that it had now been "quite significantly reduced".
Later, a British plane carrying an emergency deployment team had arrived at the Hassi Messaoud airport, about 300 miles (480km) north-west of Amenas, the Foreign Office said.
Japanese officials were meanwhile cited as saying by the Kyodo news agency that at least 14 Japanese nationals were still missing. At least three managed to escape.
Japan's Chief Cabinet Secretary, Yoshihide Suga, expressed "deep regret" at the actions of the Algerian security forces and its foreign ministry summoned the Algerian ambassador.
Despite requests for communication and pleas to consider the hostages' safety, the UK, Japan and US said they had not been told in advance about the military assault.
Mr Cameron said the Algerian prime minister had told him that commanders had "judged there to be an immediate threat to the lives of the hostages and had felt obliged to respond".
Algerian Communications Minister Mohand Said Oubelaid said: "Those who think we will negotiate with terrorists are delusional."
Norway said eight of its nationals were currently unaccounted for. One is being treated at a hospital in In Amenas, while four escaped unharmed.
French Interior Minister Manuel Valls said two French workers were safe. It was unclear if another two were involved, he added.
The Irish government confirmed that one of its citizens was free. Five Americans had survived and left the country, US officials told ABC News. Austria also said one of its nationals had been released and was safe.
APS said about 600 local workers had been freed in the raid, but many were reportedly allowed to leave on Wednesday by the militants.
A worker from CIS Catering, which employs about 150 Algerians at the facility, told French media he had hidden under the bed in his room for 40 hours before being rescued.
"I put boards everywhere. I had food, water, and I did not know how long I would stay there."
"When the soldiers came to get me, I did not even know it was over. They were with colleagues, otherwise I would never have opened the door," he added.
A statement purporting to come from the kidnappers says the raid was carried out in retaliation for the French intervention against Islamist groups, including al-Qaeda in the Islamic Maghreb (AQIM), in neighbouring Mali.
But BBC security correspondent Gordon Corera says the kidnapping was a complex operation which is unlikely to have been planned and carried out since the surprising French intervention in Mali last Friday.
Mr Oubelaid said the militants were intent on "destabilising Algeria, embroiling it in the Mali conflict and damaging its natural gas infrastructure."
Algerian officials said they were operating under orders from Mokhtar Belmokhtar, who was a senior AQIM commander until late last year.
On Friday morning, a spokesman for al-Mulathameen (The Brigade of the Masked Ones) told ANI that it would carry out further operations. He warned Algerians to "stay away from the installations of foreign companies as we will strike where it is least expected".