The UK Foreign Office said the “terrorist incident” near In Amenas was “ongoing”.
Algerian state media said four hostages and several militants were killed when troops backed by helicopters attempted to free them on Thursday afternoon.
The militants had claimed to be holding 41 foreigners. At least four were freed but the fate of many others is unknown.
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 by helicopter gunfire in Thursday’s operation.
Norwegian Foreign Minister Espen Barth Eide said: “Parts of the plant are under Algerian authorities’ control, and other parts are not. This information is changing by the hour.”
The indications on Thursday night were that the military element of the operation had concluded, and that it had moved to the search phase.
But there are now some unconfirmed reports that a small group of militants and hostages remain, possibly near the gas compressor at the main gas plant.
It had always been reported that hostages were being held at different locations.
UK government sources said they were trying to establish the fate of as many as 20 British people and were bracing themselves for multiple casualties.
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.
Norwegian Prime Minister Jens Stoltenberg said the Algerian officials had said “they felt they had no choice but to go in”.
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.
APS said about 600 local workers had been freed in the raid, but many of those were reportedly allowed to leave on Wednesday by the militants.
The militants said they had seized the foreigners in retaliation for France’s military intervention in Mali, where its forces have been battling Islamists since last week.
Algerian Communications Minister Mohand Said Oubelaid said the militants were intent on “destabilizing Algeria, embroiling it in the Mali conflict and damaging its natural gas infrastructure.”
Algerian officials said the group was operating under orders from Mokhtar Belmokhtar, a senior commander of al-Qaeda in the Islamic Maghreb (AQIM) until late last year.
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 40 km (25 miles) south-west of the town of In Amenas and 1,300 km (800 miles) south-east of Algiers.
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