An Islamist website claiming to be linked to the group holding Ken Bigley and two Americans says one of the Americans has been killed.
The website carries a nine-minute video purporting to show the man being beheaded.
Earlier, Tony Blair said Britain would not give in to the hostage takers.
The Reuters news agency reports a US official has confirmed the body of one of the American hostages has been recovered.
A statement on the website said: “The group will next behead the others”.