Their prisoner, Edwin Dyer, had been abducted four months earlier with three other European tourists after they left the Festival in the Desert, the annual concert of Tuareg folk music on the Mali-Niger border.
"Islam tells us to have no connection with the ungodly…Since this is so, the hostage will be executed in the name of God," he declared, according to an account by French journalist Serge Daniel.
Dyer had been seized with Gabriella Barco Greiner and Werner Greiner from Switzerland, and 76-year-old Marianne Petzold, a retired teacher from Germany. But although they were kidnapped together, their fates were very different.
"I got out slowly because I didn't want to give in too easily," she says. She lay down in the sand until the tribesmen ordered her to climb on to a truck littered with bullet shells and Kalashnikovs. As she struggled to obey, one of the men pushed her and she fell and broke her arm.
"They must have had our passports before we arrived," says Petzold.
The group kept moving and, for a couple of days, stopped at a little valley at the edge of a mountainous plateau. The hostages lay on a blanket in the shade of two trees. There, they met a short, bearded man in his 40s called Abdelhamid Abou Zeid, who was described to them as one of the top commanders of al-Qaeda in the Islamic Maghreb (AQIM).
They verified Petzold's identity by sending questions about a dog and her family.
What happened after that is unclear. Security experts believe a payment was probably made for Petzold, though German officials have never commented on the case. But after three months in captivity, Marianne Petzold and Gabriella Greiner were released. (Greiner's husband Werner was held for another two months and released in July.) With Petzold in agony from a scorpion sting, the women began a long car ride.
In 2009, the Swiss government denied paying any ransom for the hostages' release. "Swiss officials credited Mali President Amadou Toumani Toure with securing Werner Greiner's release and insisted Switzerland had neither negotiated nor paid a ransom for him," Agence France Presse reported at the time.
Delegation had approved funds of three million [Swiss] francs [$3.2m, £1.9m] that the Federal Council had previously requested in connection with the case of Swiss hostages held in Mali".
"I know that this is difficult for families when they are the victims of these terrorists - but I'm absolutely convinced from what I've seen that this terrorist organizations, and indeed others around the world, have made tens of millions of dollars from these ransoms - and they spend that money on arming themselves, on kidnapping more people and on plotting terrorist outrages, including in our own country."
Initially, his kidnappers demanded the UK government pay $10m (£6m) for his release, according to Serge Daniel, who interviewed local tribesmen who were present at negotiations for his book AQIM: The Kidnapping Industry.
Dyer's hands were tied together. He shouted. Two shots rang out. It's unclear if the shots killed Dyer. Then he was beheaded.
"Edwin didn't deserve to be killed. He was simply the wrong nationality. Had he been German, French, anything else, he would have lived," says his younger brother, Hans Dyer, a 53-year-old British schoolteacher who acted as the Dyer family's representative with hostage negotiators. "And it all came down to money in the end."
The data they have collected suggests ransoms totalling at least $30m (£18.3m) have been paid since 2008 in connection with these kidnappings and that the going rate for a single Western hostage in the region is now about $2m (£1.2m).
"So they paid the money. Then the governments say, 'Well, we didn't pay the money.' So did the family pay the money? Did friends pay the money? Was money taken out of aid accounts in Mali so that Mali could pay the ransom and then be reimbursed?" she asks.
"It's very hidden the way it happened but nobody is released unless the ransom is paid or unless the kidnappers receive some benefit."
"Let's put it this way… suddenly, it was rumoured that some of the intermediaries had new Land Rovers. The cars would be a payoff," she says.
Islamic State (IS) militants initially asked for $100m (£61m) for US journalist James Foley. But people close to him believed IS would have accepted far less, possibly even $5m (£3m).
"We didn't believe the $100m demand was the final offer and we didn't think they would harm Jim because of the significant value for him. Sadly, that wasn't the case," says Philip Balboni, chief executive of GlobalPost, the Boston-based news organization Foley often reported for.
"It's irresponsible on the parts of these governments. It has clearly created this moral hazard and increased the desirability to terrorists of your own citizens.
The AQIM commander and leader of the gang who held Petzold and Dyer hostage, Abou Zeid, was killed in Mali in 2013 during fighting with Chadian and French forces.