Boris Johnson's father Stanley has joined the campaign to save Geronimo the alpaca as animal rights protesters prepare to march on Downing Street later on Monday.
Health officials have ordered the animal to be put down after it twice tested positive for bovine tuberculosis.
But owner Helen Macdonald, who imported Geronimo from New Zealand, claims the tests are false, is refusing a third and says she won't allow her beloved camelid to be destroyed.
Thousands of activists have signed a petition calling on the prime minister to save Geronimo from being culled.
Pledging his support for the campaign, Mr Johnson senior said the Department for Environment and Rural Affairs (Defra) must be prevented from carrying out the "murderous errand".
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“Tear up that threatening letter, minister,” Mr Johnson Snr wrote in a message to environment secretary George Eustice in The Sun.
"Write another one, a nice friendly one. Give Geronimo a new test. That’s all Helen Macdonald wants. Is that too much to ask?”
Last week, Ms Macdonald lost her final appeal to save her pet at the High Court in London and now a warrant has been signed for its destruction.
Kwasi Kwarteng, the business secretary, said he didn't know where Mr Johnson Snr's intervention was "coming from".
Answering questions on Geronimo’s case, Mr Kwarteng added: “My understanding is that the alpaca was tested positive for TB and the rules are that they have to be culled because bovine TB is really, really damaging to farmers and people who make their livelihoods in agriculture and that's why we have the policy.”
A protest will start at 2pm on Monday at Defra's headquarters at Smith Square in Westminster before heading to the gates of Downing Street.
The demo is being organised by members of the Born Free Foundation, the Alpaca Society, and practising vet and bovine TB policy expert, Dr Iain McGill.
The demonstrators will be joined by a number of alpacas, who have been trained to walk with people and are comfortable around crowds, the organisers said.
The campaigners believe that Geronimo is free of TB and that Defra's tests are highly likely to be inaccurate.
They are demanding a different type of test be used to prove Geronimo's disease status before the animal is culled.
Speaking before the protest, Dominic Dyer, from the Born Free Foundation, said: "Defra has known for many years that the TB skin test could be leading to false positive TB results in alpacas.
"However rather than allow Geronimo to be tested for TB using a more accurate Actiphage PCR blood test, Defra Secretary George Eustice continues to order his death to avoid greater scrutiny over the many failures in the government bovine TB control policy in cattle, alpacas and badgers."
The outcry over Geronimo's fate prompted Mr Eustice, who comes from a farming background, to write an article in the Mail on Sunday about his own experiences with bovine TB.
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"Each week on average, we have to remove more than 500 cattle from herds due to infection in England alone. Behind every one of those cases is a farmer who has suffered loss and tragedy," he said.
"Farmers understand that infected animals are a risk to the remainder of their herd, so while the loss of individual animals is always a tragedy, the farming communities have worked with our Government vets in this arduous but necessary endeavour."