BP, the Norwegian company Statoil and the Algerian state oil company Sonatrach, operate the gas field and a Japanese company, JGC Corp, provides services for the facility.
Japan's Prime Minister Shinzo Abe protested the military raid as an act that "threatened the lives of the hostages," according to a spokesman.
Jean-Christophe Gray, a spokesman for Cameron, said Britain was not informed in advance of the raid.
One Irish hostage managed to escape: electrician Stephen McFaul, who'd worked in North Africa's oil and natural gas fields off and on for 15 years. His family said the militants let hostages call their families to press the kidnappers' demands.
"He phoned me at 9 o'clock to say al-Qaida were holding him, kidnapped, and to contact the Irish government, for they wanted publicity. Nightmare, so it was. Never want to do it again. He'll not be back! He'll take a job here in Belfast like the rest of us," said his mother, Marie.
Dylan, McFaul's 13-year-old son, started crying as he talked to Ulster Television. "I feel over the moon, just really excited. I just can't wait for him to get home," he said.
At least one Filipino managed to escape and was slightly injured, the Philippine Foreign Affairs Department said. Spokesman Raul Hernandez said he had no information about any fatalities.
Algerian forces who had ringed the Ain Amenas complex had vowed not to negotiate with the militants, who reportedly were seeking safe passage. Security experts said the end of the two-day standoff was in keeping with the North African country's tough approach to terrorism.
"Algerians clearly were not willing to compromise with the terrorists and not willing to accept the idea of coping with the situation for days and days," said Riccardo Fabiani of Eurasia Group. "Algerians never had problems causing a blood bath to respond to terrorist attacks."
Phone contacts with the militants were severed as government forces closed in, according to the Mauritanian agency, which often carries reports from al-Qaida-linked extremist groups in North Africa.
A 58-year-old Norwegian engineer who made it to the safety of a nearby Algerian military camp told his wife how militants attacked a bus Wednesday before being fended off by a military escort.
"Bullets were flying over their heads as they hid on the floor of the bus," Vigdis Sletten told The Associated Press in a phone interview from her home in Bokn, on Norway's west coast.
Her husband and the other bus passengers climbed out of a window and were transported to a nearby military camp, she said, declining to give his name for security reasons.
News of the bloody Algerian operation caused oil prices to rise $1.25 to close at $95.49 a barrel on the New York Mercantile Exchange, and prompted energy companies like BP PLC and Spain's Compania Espanola de Petroleos SA to try to relocate energy workers at other Algerian plants.
Algerian Interior Minister Daho Ould Kabila said the 20-odd militants entered the country from nearby Libya in three vehicles, in an operation commanded by extremist mastermind Moktar Belmoktar, who is normally based in Mali.
"The Algerian authorities have expressed, many times, to the Libyan authorities, its fears and asked it a dozen times to be careful and secure borders with Algeria," Kabila was quoted as saying on the website of the newspaper Echourouk.
The militants made it clear that their attack was fallout from the intervention in Mali. One commander, Oumar Ould Hamaha, said they were now "globalizing the conflict" in revenge for the military assault on Malian soil.
France has encountered fierce resistance from the extremist groups in Mali and failed to persuade many allies to join in the actual combat. The Algeria raid could push other partners to act more decisively in Mali — but could also scare away those who are wary of inviting terrorist attacks back home.
Associated Press writers Karim Kabir in Algiers, Bradley Klapper, Kimberly Dozier and Robert Burns in Washington, Lori Hinnant and Elaine Ganley in Paris, Shawn Pogatchnik in Dublin, Bjoern H. Amland in Oslo, Norway, Mari Yamaguchi in Tokyo and Cassie Vinograd and Jill Lawless in London contributed to this report.