At least 30 hostages and 11 members of an al-Qaeda-affiliated group were killed when Algerian forces stormed a desert gas plant to free the captives, drawing international attention to al-Qaeda in North Africa.
Eight Algerians and seven foreigners, including two British, two Japanese and a French national, were among the dead, an Algerian security source said.
The military says some of the gunmen who took hundreds of hostages at the gas facility, are still holed up inside.
Nine foreign nationals were released but the fate of a number of those who had been held by the fighters remains unclear.
Stephen McFaul from the Republic of Ireland is one of the foreign nationals who have been released
The hostages included Algerians, as well as foreigners from at least nine countries - including the US, Britain and Japan.
At least 22 hostages are still missing - eight from Norway and 14 from Japan.
Japanese Prime Minister Shinzo Abe cut short a visit to Indonesia on Friday, reports said, to fly home and deal with the hostage crisis in Algeria in which numerous Japanese are caught up.
The Japanese government criticised the Algerian army for the bloody end to the hostage crisis.
Japan's foreign ministry also summoned the Algerian ambassador demanding answers over the rescue operation
Yoshihide Suga, the Chief Cabinet Secretary, said: "There is still much confusion in the information but we are receiving reports of casualties.
"We deeply regret the actions taken by the Algerian military."
Communication Minister Mohamed Said said troops had been forced to act after talks with the kidnappers failed.
He said many fighters had been killed in the operation at the In Amenas gas field.
Algerian officials says those behind the attack were part of an Al-Qaeda linked group and included Egyptian, Algerian and Tunisian nationals.
The government said it was forced to launch the military operation because the fighters had threatened to blow up the gas plant.
The Philippines government says one Filipino managed to escape with a Japanese citizen before the military operation started.
"We have also received a report from our embassy in London that around 34 Filipinos working with different companies in the gas field are being evacuated by chartered plane to London via Parma, Italy," Paul Hernandez, spokesperson of the Philippines department of foreign affairs, said.
Oil giant BP has chartered two flights from Algeria to London, while a US plane landed at an airport near the desert gas plant.
The plane will evacuate Americans caught up in the crisis, a local source said.
France Interior Minister Manuel Valls said that two French workers were back safe from Algeria, adding that "very few" were working at the gas plant at the time of the attack.
"There were very few French on this especially sprawling base," the minister told French radio.
"We have news from two of those who are back. Regarding the two others, if there were two others, we don't have more
information at this stage and hope to have more later in the morning," he added.
A British diplomatic source said that they had not received word from Algeria that the hostage crisis ended.
"The terrorist incident in Algeria remains ongoing," said a Foreign Office spokeswoman, adding that British Prime Minister David Cameron would chair a meeting of Britain's COBRA emergency committee on Friday.
The Masked Brigade said its fighters seized the workers on Wednesday in retaliation for Algeria letting France use its airspace to launch operations against rebels in northern Mali , but security experts said the raid appeared to have been planned well in advance.
Christina Hellmich of Reading University talks to
Al Jazeera about al-Qaeda's role in the region
The fighters came from Libya, according to the Algerian interior minister.
"According to the information we have, the terrorist group which attacked the In Amenas site came from Libya," Dahou Ould Kablia told Algeria's Arab-language daily Echorouk.
Kablia had said on Wednesday the kidnappers were from the region, denying that they came from Libya or from Mali as some of them claimed.
Algeria's official APS news agency said nearly 600 Algerian workers and four foreign hostages - two Britons, a Frenchman and a Kenyan - had been freed during the operation. The Irish foreign ministry said an Irish man had also been freed.
In Washington, White House Press Secretary Jay Carney said the US administration was "concerned about reports of loss of life and are seeking clarity from the government of Algeria".
The fighters, communicating through media in neighbouring Mauritania, said they had dozens of men armed with mortars and anti-aircraft missiles in the compound and had rigged it with explosives.
"We hold the Algerian government and the French government and the countries of the hostages fully responsible if our demands are not met, and it is up to them to stop the brutal aggression against our people in Mali," read one statement carried by Mauritanian media.
A Briton and an Algerian were killed on Wednesday, after fighters launched an ambush of a bus carrying employees from the gas plant to the nearby airport.
The In Amenas gas field is jointly operated by British oil giant BP, Norway's Statoil and Algeria's Sonatrach.
France launched a major offensive against the rebel group Ansar al-Dine in Mali on January 11 to prevent them from advancing on the capital, Bamako.
Algeria had long warned against military intervention against the rebels, fearing the violence could spill over the border.