Geronimo the alpaca has been handed a 24-hour reprieve, delaying his execution by a day.
The animal has twice tested positive for bovine tuberculosis, and the Department of Food, Environment and Rural Affairs (Defra) ordered he be euthanised.
His owner, Helen Macdonald, who imported him from New Zealand, believes the tests are returning false positives, but was refused permission to have him tested a third time.
Last week, Ms Macdonald lost her final appeal to save her beloved pet at the High Court in London and a warrant was signed for his destruction.
She was yesterday denied a stay of execution by the High Court.
It meant Defra were allowed to come to her farm in Wooton Under Edge, Gloucestershire, and kill the animal from 4.30pm today.
But this afternoon, Helen was told by the Department of Environment, Food and Rural Affairs (Defra) that officials would not attempt to enforce the destruction warrant before 5pm on Friday
Helen has received an outpouring of support from the members of the public who oppose plans to kill Geronimo.
Nearly 100,000 people have signed a petition calling on Boris Johnson to halt the killing.
Around 30 people - including fellow alpaca farmers who had lost animals in similar circumstances - gathered outside Defra's headquarters in Smith Square, Westminster.
Several alpacas who were reportedly due to attend the march were not brought along due to safety concerns.
Protesters marched past the Houses of Parliament to the gates of Downing Street on Whitehall.
Some carried banners reading "We stand with Geronimo" and "Eustice, admit you're wrong."
The campaigners believed that Geronimo was free of TB and that Defra's tests are highly likely to be inaccurate.
They demanded a different type of test be used to prove Geronimo's disease status before his death.
But Downing Street insisted that all the evidence on the animal's condition had been "looked at very carefully."
The Prime Minister's official spokesman said: "We know how distressing losing animals to TB is for anyone. That is why the Environment Secretary has looked at this extremely carefully and interrogated all the evidence.
"The fact remains that Geronimo has sadly tested positive twice using a highly specific and reliable and validated test.
"This is something the Environment Secretary has looked at very carefully."
Speaking from her farm, Ms Macdonald criticised the Government for refusing to change its mind.
"Unfortunately they are still misquoting data," she said earlier.
"What they did to Geronimo was not a validated test - they knew what they were doing.
"I do not want to be singled out. It's about making decisions that have backfired on them and taking it out on Geronimo and causing him harm and me and my family harm purely because they didn't listen to us four years ago when they thought there was a problem.
"We are just asking to have him tested with something appropriate. I get they have policy to follow but there are other ways, and they don't have to kill him. He is safe in isolation here.
"They've always been happy with that and he's not a public health risk. They won't test his friends, so they are obviously not worried that he is going to give them TB.
"No-one has died here from TB in four years, so I just don't understand why it has to be this drastic."
At her farm, friends, family and supporters joined her to protest against Geronimo's fate.
As well as alpacas, badgers have been a victim of the fight against bovine TB, with mass culling employed to stop the spread since 2013, sparking a huge public backlash.
Campaigners called for the Prime Minister to force Environment Secretary George Eustice to halt the killing and immediately implement the latest bovine TB tests for all suspected cases.
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They also want to see an end to all further badger cull licences in favour of a vaccination programme for 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.
"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."
