Fears for the safety of the kidnapped BBC journalist Alan Johnston increased yesterday amid suggestions that he had been “sold” to Islamic militants shortly before unconfirmed claims were made that he had been killed.

The Foreign and Commonwealth Office said that it was “urgently investigating” a claim by an Islamist group that it had killed the BBC’s Gaza-based correspondent and that it would release a video of his death.

Although the Kataeb al-Jihad al-Tawheed (the Brigades of Holy War and Unity) group is not known in Gaza, the name has been used elsewhere in the Middle East by organisations linked to al-Qaeda.

Johnston, 44, has been missing longer than any other Western hostage in Gaza since he was seized at gunpoint on March 12. No group had admitted responsibility for his kidnapping before the statement on Sunday.

In its message the group said that it killed Johnston to support its demand for the release of Palestinian prisoners held by Israel. The group said that it had sent its demand to the Palestinian and British governments, although officials from both offices denied receiving any message.

Johnston’s parents yesterday appealed for an end to their ordeal. Graham and Margaret Johnston, who live in Cairndow, Argyll, said: “This is a desperately worrying time for us.

We make a heartfelt appeal to anyone who may have knowledge of Alan’s situation and wellbeing to contact the authorities in Gaza.

“Our son has lived and worked among the people of Gaza for the last three years to bring their story to the outside world and we ask every one of them to help end this ordeal.”

Palestinian security sources have identified the Dagmoush crime clan as the prime suspect in the kidnapping of Johnston. The clan has carried out kidnappings in the past — including two journalists employed by the American Fox television network last summer — to extract promises of money or weapons from the Palestinian Authority.

The clan was once allied with Hamas, but switched loyalties last summer when two of its members were killed by Hamas gunmen. There were rumours that the family had sought revenge by kidnapping Johnston and embarrassing the Hamas-led Government. The Dagmoush family has denied any involvement.

There was speculation over the weekend that the clan had decided to “sell” Johnston to a jihadist group, a tactic that has been used in Iraq.

One source said it was feared that “external forces” had become involved since Mahmoud Abbas, the Palestinian President, said last week that he had “credible evidence” that Johnston was “safe and well”.

Palestinian officials said yesterday that they were still treating claims of Johnston’s killing as a hoax, pointing out that the execution tape that the group claimed to possess had yet to materialise.

Saeb Erekat, a chief Palestinian negotiator, said: “We don’t believe they [Kataeb al-Jihad al-Tawheed] exist. Nobody’s ever heard of them before. We have every reason to believe that Mr Johnston is still alive. All the people I have spoken to in intelligence and security have assured me that this is the case, though they can’t get into details of how they come by this knowledge.”

Thousands of BBC staff across Britain held a silent vigil in support of Johnston yesterday at 2.15pm, the exact time that the reporter was snatched. In Beirut, dozens of Lebanese and foreign journalists staged the latest protest in solidarity with Johnston, and in Brussels, scores of journalists attended a rally.

Johnston was shortlisted yesterday in the Broadcasting Journalist of the Year category for the London Press Club Awards.

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