The Algerian military assault left "several people" killed or wounded but freed a "large number" of hostages, according to communications minister Mohamed Said, as special forces took control of a residential compound at the complex.
Hundreds of hostages were being held at the compound, part of the sprawling In Amenas site, after Islamist militants took control of the gas plant on Wednesday purportedly to avenge a French-led offensive in Mali.
Algerian officials said soldiers were still surrounding the site's main gas facility, which was yet to be secured in the air and ground assault.
Algerian reports said nearly 600 local workers and four foreigners -- two from Britain, one from France and one from Kenya -- were freed during Thursday's operation.
One man from Northern Ireland escaped. According to his brother, Stephen McFaul fled when the convoy in which he was travelling came under fire from the army, and had earlier "had explosives tied around his neck".
A total of 41 foreigners had been reported among the hostages. The huge plant employs workers from Britain, France, Italy, Japan, Norway and the United States among others, and there was widespread anxiety at the fast-moving developments.
British Prime Minister David Cameron, who cancelled a key speech on European policy to monitor the crisis, described a "very bad situation" at the site near Algeria's border with Libya.
"Already we know of one (Briton) who has died," Cameron said. "It is a very dangerous, very uncertain, a very fluid situation, and I think we have to prepare ourselves for the possibility of bad news ahead."
Foreign governments said Algeria gave them no prior warning of the raid. A senior US official said Washington "strongly encouraged" the authorities to make the safety of the hostages their top priority.
Japan's government also urged Algiers to protect the hostages, arguing that the army raid was "regrettable" and that there was no clear information emanating from the scene.
The kidnappers said 34 captives had died in the assault, but this was impossible to confirm. They told Mauritanian news agency ANI they would "kill all the hostages if the Algerian forces succeed in entering the complex".
The site is run by British oil giant BP, Norway's Statoil and Algerian energy firm Sonatrach. Japanese construction company JGC said it had confirmed the safety of three out of its 17 Japanese staff, and one Filipino.
'The Uncatchable' mastermind
Veteran Islamist fighter Mokhtar Belmokhtar, a one-eyed Algerian jihadist with Al-Qaeda ties, has claimed responsibility for launching Wednesday's attack.
Belmokhtar, dubbed "The Uncatchable" by French intelligence and "Mister Marlboro" for his cigarette smuggling, was until recently one of the leaders of Al-Qaeda in the Islamic Maghreb.
But he was pushed out of the organisation towards the end of last year and set up a group called "Signatories in Blood". He has been blamed for previous abductions and the killings of both Algerians and foreigners.
The chief hostage taker on the ground, Abu al-Baraa, was reported killed in the Algerian operation by ANI, which often carries reliable reports from Al-Qaeda linked groups.
"We demand the Algerian army pull out from the area to allow negotiations," Abu al-Baraa had earlier told Al-Jazeera news channel.
But Algeria insisted it would not negotiate with "terrorists".
The hostage drama dragged Algiers and Western powers into the Mali conflict, taking the spotlight off French and government troops battling the Islamists in control of the country's vast desert north.
The rebels have held the north since April last year and moved south into government-held territory last week, prompting France to intervene in its former West African colony before they could threaten roads to Mali's capital Bamako.
The UN special envoy for the Sahel, Romano Prodi, said the French air and ground intervention in Mali was the only way to stop Islamists creating "a terrorist safe haven in the heart of Africa".
In Brussels, French Foreign Minister Laurent Fabius said EU countries may provide troops to help France.
On Thursday, more French troops poured into Mali, boosting their number to 1,400, Paris said. At full strength the force will reach 2,500 soldiers.