The British victims - named as Ruth Williamson, Margaret Whitehouse and Peter Rowe - died after the Yemenis staged a rescue attempt despite a request from Britain that force should not be used. Officials in Aden said they took the option only when the kidnappers began killing their prisoners. Last night, the Foreign Office was advising Britons to leave Yemen.
Few other details were released about the dead and injured. Mr Rowe died in hospital from wounds. It was unclear whether he was injured by his captors or during the shoot-out. Three of the kidnappers were killed and four taken prisoner. The attack came as the bodies of three Britons and a New Zealander, telecommunications workers murdered by their kidnappers in the breakaway Russian republic of Chechnya, were flown home.
In a statement issued last night, Robin Cook, the Foreign Secretary, said: "I am deeply shocked at the news of the casualties suffered by the group of tourists abducted in Yemen."
"This is an agonising situation for the families, and our sympathies and concerns rest with them, especially the bereaved. We are doing everything we can to establish the full facts."
Two of the freed hostages, one British and one American woman, were in hospital last night. The other 10 survivors were recovering from their ordeal in the Movenpick Hotel in Aden, said the British embassy deputy head of mission, David Pearce. "They are obviously in a state of severe shock, and I mean severe shock."
British and American volunteers were talking with them to try to help them cope with their trauma, he said. "They are uninjured but obviously very tired, very stunned and in need of a good meal, a good rest and someone to talk to. They have been through an awful experience."
As soon as the survivors are fit, it is thought they will be asked who began shooting first. In a statement, the Yemeni Interior Ministry said the kidnappers killed the hostages after refusing attempts at negotiations. Yemeni sources said the kidnappers, from the Al-Fadl tribe, belonged to Islamic Jihad.
The hostages - six British women, six British men, two American women and two Australian men - were kidnapped on Monday. Their five-car convoy containing 17 tourists on a trip organised by a British company was ambushed by 18 kidnappers armed with Kalashnikov rifles and bazookas near Mawdiyah, 175 miles south of the capital, Sanaa.
Warning shots were fired, but no one was hurt, and the lead vehicle - in which the British tour leader, David Knott, was travelling - escaped to raise the alarm.
As negotiations for their release were under way yesterday, the Yemenis said they knew of their whereabouts. At 11am GMT, Victor Henderson, the British Ambassador, met General Hussein Mohammed Arab, the Yemeni Interior Minister, and urged him to desist from the use of force.
A Foreign Office spokesman said: "The Ambassador made it clear to the Yemeni authorities that no violence should take place, the safety of the hostages was paramount and that no rescue attempt should be made that put the hostages' lives at risk."
But more than 200 soldiers were already in place around the hostages' hide-out in an area known as al-Wadeaa, 250 miles from the capital. According to the Yemenis, the kidnappers were attacked when they began shooting the hostages.
An unnamed Yemeni official told the Reuters news agency: "The operation started after abductors started killing hostages ... They killed two, and then our forces stormed them to prevent an escalation of the situation and the killing of more hostages."
After the shoot-out, security forces detained scores of suspected Islamic extremists, security officials said.