State-run APS news agency said those freed at the In Amenas installation included 573 Algerians and more than half of 132 foreign workers.
The militants remained holed up at the site and the Algerian army wanted a “peaceful end” to the crisis, APS said.
At least four foreign workers died when troops moved in on Thursday.
A “comprehensive total” of the hostages still held was not available and some of them had taken refuge at various points around the site, a security source told APS.
The installation had been put out of action to avoid the risk of an explosion, the agency reported.
Meanwhile, BP said on Friday that hundreds of workers from international oil companies had been evacuated from Algeria on Thursday and that many more would follow.
On Friday morning, a spokesman for the group thought to be behind the attack told the Mauritanian ANI agency 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”.
Algeria has yet to give precise casualty figures from Thursday’s 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 ANI 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 40 km (25 miles) south-west of the town of In Amenas and 1,300 km (800 miles) south-east of Algiers.
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”.
Japanese officials were meanwhile quoted 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.
David 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.
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 neighboring Mali.
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.
Algerian officials said the militants were operating under orders from Mokhtar Belmokhtar, who was a senior AQIM commander until late last year.
Foreign citizens involved
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