Communication Minister Mohamed Said said "several people" had been killed or wounded and a "large number" of hostages freed at a site jointly run by British oil giant BP, Norway's Statoil and Algeria's state energy firm Sonatrach.
The huge plant employed workers from Britain, America, Japan, France, Italy, Norway and others, and their governments and employers expressed concern.
"We were not aware of the raid in advance," a senior US official told AFP, adding that American officials "strongly encouraged" the Algerian authorities to make the safety of the hostages their top priority.
Japanese construction firm JGC said it had confirmed the safety of three Japanese staff in Algeria, while the whereabouts of another 14 was unknown.
The kidnappers, who claim ties with Al-Qaeda, said the army air and ground assault on the complex near the Libyan border had left 34 hostages dead, but this was impossible to confirm independently.
The kidnappers told the Mauritanian news agency ANI they would "kill all the hostages if the Algerian forces succeed in entering the complex." They claim to have acted to avenge a French-led offensive against Islamists in Mali.
Algeria's Interior Minister Dahou Ould Kablia said the attackers had come from across the nearby Libyan border, citing intelligence reports.
British Prime Minister David Cameron, who cancelled a key speech on European policy to monitor the crisis, described a "very bad situation" at the compound, where a number of British citizens had been taken hostage.
"Already we know of one who has died. The Algerian armed forces have now attacked this compound," 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."
French President Francois Hollande said he was receiving regular updates on the "terrible" situation, which was strongly condemned by Japan.
Italian Foreign Minister Giulio Terzi dubbed the hostage deaths an "atrocious consequence of a vile act of terrorism."
Islamists seized the site on Wednesday in an attack that left two dead.
Algerian media reports said nearly 600 Algerian workers and four foreigners -- two from Britain, one from France and one from Kenya -- were freed during Thursday's operation. The Irish government said one of its citizens was freed.
A total of 41 foreigners had been reported among the hostages.
-- 'Mister Marlboro' --
Veteran Islamist fighter Mokhtar Belmokhtar, a one-eyed Algerian jihadist with Al-Qaeda ties, has claimed responsibility for launching the attack.
Belmokhtar, dubbed "The Uncatchable" by French intelligence and "Mister Marlboro" for his illicit cigarette smuggling, was until recently one of the leaders of Al-Qaeda in the Islamic Maghreb (AQIM).
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 fast-moving hostage drama dragged Algiers and several top Western powers into the Mali conflict, taking the spotlight off French and government troops battling the Islamists controlling the country's vast desert north.
The UN special envoy for the Sahel, Romano Prodi, said that 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 in its former West African colony.
On Thursday, more French troops poured into Mali, boosting their number to 1,400, the defence minister said. At full strength the force will reach 2,500 soldiers.
A first troop contingent from Chad arrived in Mali while nearly 100 Nigerian and Chadian soldiers were on their way Thursday to make up an African force set to reach over 5,000 troops.
A French defence ministry source said there were "clashes in several areas" but "no fighting in the area of Diabaly", 400 kilometres (250 miles) north of the capital Bamako, where French forces were in action on Wednesday.
Islamist rebels have controlled northern Mali since April last year and moved south into government-held territory last week prompting France to intervene before they could threaten roads to the capital Bamako.