One of the two American hostages seized with the British engineer Ken Bigley in Baghdad was beheaded last night.

A video of the incident was posted on the internet by the militant group holding the three men.

The terrorists then gave warning that the remaining two hostages, Bigley and Jack Hensley, the other American, would be killed within 24 hours if their demands were not met.

Last night Bigley's brother and son appealed to directly to Tony Blair to do more to save his life.

When asked about the government's efforts to secure Bigley's release, the prime minister said: "I don't think it is sensible for us to say anything at all at the present time, except to say, obviously, that we are focused on doing what we can."

Last night a Foreign Office spokesman said: "The government utterly condemns the kidnapping and murder of all innocent civilians. This appalling crime strengthens our resolve to work with the Iraqi government and people to bring security, stability and democracy to Iraq."