"We announce that we have successfully staged a large-scale attack in response to... the crusade being waged by French forces in Mali," said a statement on a Mauritanian website by a group calling itself "Signatories for Blood" -- the name of a katiba, or combat unit, led by Algerian national Mokhtar Belmokhtar, a former leader of Al-Qaeda in the Islamic Maghreb (AQIM).
The statement claimed there were "more than 40" foreign hostages, whom it called "crusaders", including seven Americans and two British.
"We hold Algeria and the hostages' countries responsible for any delay in meeting our conditions, the first of which is a halt to this aggression against our people in Mali," it said.
Mauritanian media separately reported Islamists as saying they were holding 41 hostages.
The statement by "Signatories for Blood" was published on a website called Alakhbar, which often carries material from Islamist groups.
"Algeria was chosen for this operation to teach (Algerian President Abdelaziz) Bouteflika that we will never accept the humiliation of the Algerian people's honour... by opening Algerian airspace to French planes," it said.
France said Sunday that Algeria had agreed to allow French warplanes to cross its airspace on their way to Mali for raids on the Islamist rebels that seized the north of the country, which borders Algeria to the southeast, in April last year.
"This operation is also part of a worldwide campaign of struggle against Jews and crusaders," the statement added.
One Briton and an Algerian were killed in the attack on the In Amenas gas field, Algerian Interior Minister Dahou Ould Kablia said. Six people were also wounded.
The gas field is jointly operated by British oil giant BP, Norway's Statoil and state-run Algerian energy firm Sonatrach. Production was shut down after the attack on the site, which is located 1,300 kilometres (810 miles) southeast of Algiers, close to the Libyan border.
The attack was the first reprisal by the Islamists for the French assault on Mali, which began on January 11.