Gordon Brown, Britain's prime minister, condemned the killing as an "appalling and barbaric act of terrorism" and said it reinforced Britain's "commitment to confront terrorism".
In a statement issued on Wednesday, Brown said: "We have strong reason to believe that a British citizen Edwin Dyer has been murdered by an al-Qaeda cell in Mali.
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"I want those who would use terror against British citizens to know ... we will pursue them relentlessly"
Gordon Brown, British prime minister
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"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."
Abu Qatada has been held in Britain since 2005 and is awaiting extradition to Jordan, where he was convicted of terrorism offences and faces life in jail.
Last month, the Algerian media reported that al-Qaeda in the Islamic Maghreb (AQIM) was demanding $14.21m in exchange for the Briton and another hostage, a Swiss national, being held in Mali.