Gareth Morgan has a simple dream: a New Zealand free of cats. But the environmentalist's latest anti-feline campaign has triggered a backlash.

Morgan has called on fellow Kiwis to make their current pet cat their last in a bold attempt to save the country's native birds. He set up a website, Cats To Go, which includes an image of a kitten with devil's horns under the heading: "That little ball of fluff you own is a natural born killer".

He does not recommended owners euthanise their cats: "Not necessarily, but that is an option," he admits, but rather neuter them and not replace them when they die. The economist and well-known businessman also suggests cats remain indoors and local governments make registration mandatory.

But Morgan's campaign is not proving popular in a country that boasts one of the highest cat-ownership rates in the world. "I say to Gareth Morgan, butt out of our lives," Bob Kerridge, president of the Royal New Zealand Society for the Prevention of Cruelty to Animals, said on the television show Campbell Live. "Don't deprive us of the beautiful companionship that a cat can provide individually and as a family."

For thousands of years, New Zealand's birds flourished with no predators. Some species, such as the kiwi, even became flightless. But the arrival of mankind and its introduction of predators, including cats, dogs and rodents, has wiped out some native species and endangered many others.

"Imagine a New Zealand teeming with native wildlife; penguins on the beach, kiwis roaming about in your garden," Morgan says on his website. "Imagine hearing birdsong in our cities."

But many New Zealanders are against the campaign. On Tuesday 70% of visitors to his site voted against making their current cat their last.

The science remains unclear. Some argue that cats may actually help native birds by reducing the population of rodents, which sometimes feed on bird eggs.

Morgan's personal blog has a separate campaign to raise $1m to eradicate mice from the remote Antipodes Islands, where the rodents are the only predators.

A 2011 survey by the New Zealand Companion Animal Council found 48% of households in New Zealand owned at least one cat, a significantly higher proportion than in other developed nations. The poll put the total cat population at 1.4m.

In the US, 33% of households own at least one cat, amounting to 86m domestic cats, according to a 2012 survey by the American Pet Products Association.