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The funds raised will go to the London site and its partner zoo, Whipsnade, which staff have warned are "at risk of extinction" after 12 weeks of closure in lockdown.
Both zoos reopened a week ago, but with visitor numbers limited due to social distancing and three month's lost trade to make up for, bosses warn the zoos still risk financial ruin.
Speaking to The Sunday Times about the campaign, Sir David said: "What happens if you can't raise the money to keep the animals? What happens if you can't afford the food? Are we supposed to put them down?"
"The immediate prospect of the zoo going financially bust is too awful to think of. Are we, or are we not, a civilised community that it can't support a zoo?"
Throughout the crisis, the zoos have continued to feed and care for their animal residents without revenue from visitors.
London Zoo is home to over 18,000 animals, with the monthly food bill clocking in at around £43,500.
Bedfordshire site Whipsnade, meanwhile, houses more than 2,000 animals.
Sir David, who began his career in broadcasting by presenting the BBC series Zoo Quest in 1954, stressed the educational and scientific importance of zoos for society.
"No television programme can replace the actual reality of standing close to an elephant or for a child to understand what an elephant is," he said.
"When you stand alongside the thing, where you can smell it, you can hear its stomach rumbling - the reality of what wild creatures are."
The presenter went on to say that it would be a "scandal" if the country couldn't save the zoos from ruin.
"A zoo is a very important thing scientifically. London was the first scientific zoo in the world, founded nearly 200 years ago, and has been at the forefront of technology and advances ever since then."
"If this country can't support it, it would be a scandal," he added.
The news comes as many zoos around the country face uncertain futures.
Earlier this month, The Wild Planet Trust said it would not reopen its Living Coasts site because they did not have the funds to foot the bill for "substantial maintenance costs" incurred due to Covid-19.
There were fears that some animals would have to be euthanised but a statement from the trust confirmed that new homes for its residents had been found.
"Following the announcement on Monday that Living Coasts in Torquay, Devon will not be re-opening as a visitor attraction following its closure during the current global coronavirus pandemic, Wild Planet Trust is pleased to announce that it has already found homes for its animals.
"Living Coasts is part of a world-wide network of zoos and aquariums, and this community has come together to re-home the animals in their specialist facilities.
"The animals will not be moved immediately as moving animals to other zoos and aquariums is a complex process."