Al Qaeda's North Africa wing said on Wednesday it had carried out its threat to kill a British hostage it was holding the Sahara.
Britain said it had reason to believe the hostage, Edwin Dyer, had been killed and Prime Minister Gordon Brown condemned the killing as "a barbaric act of terrorism".
The group had said it would kill the Briton if the British government did not release Abu Qatada, a Jordanian Islamist it is holding in prison.
The hostage was killed on May 31 after a second deadline for their demands expired, the group said in a statement on a website used by al Qaeda-linked groups.
"The British captive was killed so that he, and with him the British state, may taste a tiny portion of what innocent Muslims taste every day at the hands of the Crusader and Jewish coalition to the east and to the west," the statement said.
Brown said in a statement: "We have strong reason to believe that a British citizen, Edwin Dyer, has been murdered by an Al Qaeda cell in Mali. I utterly condemn this appalling and barbaric act of terrorism."
Brown said the killing reinforced Britain's commitment to confront terrorism.
"It strengthens our determination never to concede to the demands of terrorists, nor to pay ransoms. I want those who would use terror against British citizens to know beyond doubt that we and our allies will pursue them relentlessly, and that they will meet the justice they deserve," he said.
"I have regularly discussed this case with the president of Mali -- he knows that he will have every support in rooting out Al Qaeda from his country."
Abu Qatada, named by a Spanish judge as the right-hand man in Europe of Osama bin Laden's al Qaeda network, has been held in Britain since 2005. He denies belonging to the group.
Britain has described him as a "significant international terrorist" but said it does not have enough evidence to put him on trial.
Britain's highest court ruled in February he could be deported to Jordan despite fears he may be tortured there.
Al Qaeda in the Islamic Maghreb (AQIM) has claimed responsibility for the kidnapping of two Canadian diplomats and four European tourists in the past five months. The two diplomats and two of the tourists were freed in Mali in April.
Last month, Algerian media reported AQIM was demanding 10 million euros ($14 million) in exchange for the Briton and another hostage, a Swiss national, being held in the Sahara.