The group also called for an end to France's "crusade". Chad meanwhile announced it would be sending 2 000 soldiers to fight in Mali.
After days of air strikes on rebel positions in northern Mali, controlled by the rebels since April, French and Malian ground forces battled the insurgents in the central towns of Diabaly and Konna.
But the assault on a gas field over the border in Algeria dramatically raised the stakes.
Islamists said they were holding 41 foreign hostages, including seven Americans, after their attack on the In Amenas gas field in the east of the country.
A group calling itself "Signatories for Blood" claimed the action in a post to the Mauritanian website Al-Akhbar.
The attack was in reprisal for "the crusade being waged by French forces in Mali" and for Algerian's co-operation, it said, calling for an end to the operation.
Algerian Interior Minister Dahou Ould Kablia said that one Briton and an Algerian had been killed in the attack, while another six people – a Briton, a Norwegian, a Scot and three Algerians – had been wounded.
Other reports said the hostages included Japanese, Malaysian, Norwegian and Filipino nationals. Dublin confirmed the kidnapping of an Irish national while the US state department said several of its nationals were being held.
The attackers had also demanded the release of 100 extremists held in Algeria in exchange for their hostages, a worker at the gas field site told Agence France-Presse (AFP).
The attack came less than a week after France launched its air strikes on Islamists forces in northern Mali on January 11 and just days after Algeria opened its airspace to French fighter jets engaged in the mission.
Jointly operated by British oil giant BP, Norway's Statoil and state-run Algerian energy firm Sonatrach, the gas field is located 1 300 kilometres southeast of Algiers, close to the Libyan border.
On the ground in central Mali, French troops engaged Islamist fighters in Diabaly, a town seized two days earlier by fighters led by Algerian Abou Zeid, one of the leaders of al-Qaeda in the Islamic Maghreb.
"The special forces are currently in Diabaly, in close-quarter combat with the Islamists. The Malian army is also in place," a Malian security source said on condition of anonymity.
There were also clashes near Konna, the central town Islamist forces seized last week, prompting the French intervention, security sources said.
The French military said it had secured a strategic bridge on the Niger River near the town of Markala, south of Diabaly, blocking a key route to Bamako.
French Defence Minister Jean-Yves Le Drian said the western zone around Diabaly was home to "the toughest, most fanatical and best-organised groups. It's underway there but it's difficult".
ICC launches Mali war crimes probe
The International Criminal Court said it had launched a war crimes probe on Wednesday, as rights groups and military sources denounced the extremists' use of child soldiers and use of civilians as human shields.
"Different armed groups have caused havoc and human suffering through a range of alleged acts of extreme violence," chief prosecutor Fatou Bensouda said in a statement. "I have determined that some of these deeds of brutality and destruction may constitute war crimes."
Chad announced on Wednesday it would send 2 000 soldiers to Mali, a significant boost to the African forces gathering there. "We intend to send an infantry regiment and two support battalions, which comes to around 2 000 men," Moussa Faki Mahamat told Radio France Internationale.
They would work closely with the Malian army and the multinational West African force taking shape, he added.
Nigeria will command the UN-approved 3 300-strong multinational African intervention force and has promised 900 troops. Niger, Burkina Faso, Togo, Senegal, Guinea and Ghana have also promised troops.
Some 2 000 men will arrive within the next 10 days, according to a report from a meeting of regional army chiefs seen by AFP.
Côte d'Ivoire president and Economic Community of West African States regional bloc chairperson Alassane Ouattara called for all European countries to lend support to the operation after a meeting with Chancellor Angela Merkel in Germany.
Germany has already pledged two transport planes and Italy logistical support.
France says it will ultimately send 2 500 troops, pitted against what are thought to be around 1 300 Islamic fighters.
Mali has been effectively split in two since April 2012, when extremists took advantage of a military coup in Bamako and an offensive launched by Tuareg separatists in the north to seize half the country.
The UN and aid agencies report some 370 000 Malians have been displaced by the fighting. – Sapa-AFP