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David Cameron has said the Government was doing "everything we possibly can'' to resolve the kidnapping of a tourist from Bishop's Stortford in Kenya.
The Prime Minister said the kidnap of Judith Tebbutt, 56, and the murder of her husband David Tebbutt, 58, while on holiday was "tragic''.
He said he had chaired a meeting of the Government's Cobra emergency committee about the case on Tuesday, adding that Foreign Secretary William Hague had met relatives of the Tebbutts.
Mrs Tebbutt was snatched from the remote Kiwayu Safari Village, close to the Kenyan border with Somalia, by a gang who killed Mr Tebbutt in the early hours of Sunday morning.
Earlier on Wednesday the Reuters news agency reported that Somalia's Islamist militant group al Shabaab said it was not behind the kidnapping. A senior al Shabaab official is reported to have said: "Al Shabaab has not abducted any Briton from Kenya. We believe bandits carried out the attack.''
The Prime Minister told the Commons: "I chaired a meeting of Cobra about this issue yesterday to make sure we are co-ordinating everything the Government does. We are doing everything we possibly can on this desperately tragic case.''
The retired couple's only son, Oliver, is said to be "devastated''.
MP Richard Harrington, asked Mr Cameron at Prime Minister's Questions: "What steps is the Government taking to assist in the return of Mrs Tebbutt and the apprehension of the murderers?''
Mr Cameron replied: "It's not right to air all of these issues in public but I can reassure you and all the Tebbutt family we will do everything possible to help.'' The Government's policy is not to pay ransoms to kidnappers.
Police in Kenya are reported to have arrested a man suspected of being involved in Mr Tebbutt's murder and the kidnap of his widow.