A British man being held hostage in Mali has been executed, his captors said today, prompting strong condemnation from Britain of a "barbaric" act.

Edwin Dyer, who was in his early 60s, was one of four European tourists kidnapped on January 22 as they returned from a music festival.

Messages posted on Islamic websites indicated that they were being held by Al-Qaeda in the Islamic Maghreb (AQIM), a 300-strong Islamist terror group that operates in the desert borderlands of Algeria, Mali, Niger and Mauritania.

Despite intense behind-the-scenes negotiations by British and local officials in Mali, the hostage-takers claimed that they had carried out their threat to kill Mr Dyer.

Gordon Brown said there was "strong reason" to believe that this was true. "I utterly condemn this appalling and barbaric act of terrorism," the Prime Minister said. "My thoughts are with Edwin Dyer’s family. I offer them the condolences of the whole country."

Mr Dyer, who had been working in Austria and spoke fluent German, was on holiday in West Africa with German travel operator Oase Reisen. He was abducted, along with Warens and Gabriela Greiner, a Swiss couple, and Marianne Petzold, a German woman, near the border with Niger after attending the Festival In The Desert, a celebration of music and nomad culture at Anderamboukane in Mali.

Their convoy of 4x4 vehicles was ambushed by armed men, who shot out the tyres of the first car, containing the four tourists. A second jeep containing three more tourists was hit by bullets, but the occupants were unhurt and the vehicle managed to do a U-turn and escape.

The hostage-takers then reportedly carried out a mock execution, firing a gun a bare inch from the head of the tour cook who had been travelling in the first vehicle. The cook later managed to escape and describe the incident.

At first it was believed that the hostage-takers were Tuareg rebels, bandits and smugglers who have regularly clashed with Mali's army, but in February AQIM claimed responsibility. Some analysts say the Tuareg sold the hostages to the political group.

The two female captives were released on April 22, along with two UN diplomats — Robert Fowler, a peace envoy, and Louis Guay, his aide — who had been seized in Niger in December.

Four days later the hostage-takers issued an ultimatum, warning they would kill Mr Dyer unless the UK freed the radical cleric Abu Qatada within 20 days. He is being held in Long Lartin prison in Worcestershire while he fights extradition to Jordan, where he faces terrorism charges.

On May 15 the deadline was extended by a further two weeks to May 30, and a second demand was issued, this time for a ransom of £8.6 million in exchange for the two men.

In the end, urgent efforts believed to involve the British and French security services to negotiate the safe release of the Briton failed.

In a statement issued today AQIM said: "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."

Mr Brown said: "This tragedy reinforces our 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.

"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."

David Miliband, the Foreign Secretary, said that Britain would continue working to secure the release of Mr Greiner, who is still being held. "Hostage-taking and murder can never be justified whatever the cause," he said. "This tragic news is despite the strenuous efforts of the UK team in the UK and Mali, with valuable help from international partners."

There are dissenting voices about the true story behind the kidnap. Jeremy Keenan, the editor of the security bulletin Sahara Focus and author of The Dark Sahara: America's War on Terror in Africa, alleges that AQIM is infiltrated and directed by the Algerian security services, and that the leader of the kidnappers was taking orders from Algiers. He claims that the hostage-taking was orchestrated to give the impression that North Africa was in the grip of a terrorist uprising, justifying tough measures by Algeria and its American allies.

Today the Foreign Office admitted that the security situation in the region was complex, but denied that Algeria had orchestrated the kidnap. "There has been a lot of speculation and hearsay surrounding the case," a Foreign Office spokesman said. "The picture that [Mr Keenan] describes is confused and not one that we recognise."

Britain has a policy of not paying ransoms, and there was never any prospect of the UK releasing Abu Qatada, who has been described by one judge here as "al-Qaeda's spiritual leader in Europe".

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