Al Qaeda's North Africa wing said it has carried out its threat to kill a British hostage being held in the Sahara.

The group had said it would kill the Briton, identified in its statement as Edwen Dyer, 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.

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'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 ($14.21 million) in exchange for the Briton and another hostage, a Swiss national, being held in the Sahara