It was "hugely important" to protect kiwi as they are "part of our national identity", Sir Graham said.
"When we're overseas everybody refers to us as Kiwis," he said. "It would be terrible if it became extinct. What would they call us then?"
Sir Graham said he believed the vast majority of New Zealanders would be "very passionate" about saving the flightless birds.
"It's a bit like a world cup campaign; we've just got to win this thing," he said. "And I'm sure New Zealanders will be motivated to do that. It's a very important little bird to this nation."
Kiwis for Kiwi executive director Michelle Impey said without protection from predators, 95 per cent of kiwi are killed in the wild before they are old enough to breed.
Without action, kiwi could disappear from the New Zealand mainland within a generation, she said.
"Save Kiwi Week is about raising funds for predator control. In areas that are actively managed, kiwi survival rate increases from 5 to 60 per cent," she said.
"We can reverse the decline. With support from two-legged Kiwis, our bird can flourish."
This week's campaign aims to raise $100,000 which will protect 1000 kiwi and their chicks from stoats, weasels, rats and other pests, and raise awareness of the plight of the national icon.
"Research carried out last year found that only half of New Zealanders knew that kiwi were in decline," Ms Impey said.
"All kiwi types are endangered. Some, like the rowi with a population of just 375, are critically scarce. Only a century ago, kiwi numbered in the millions."
The Department of Conservation and kiwi care groups around the country have organised events for their local community.
Those who sign up to www.kiwisforkiwi.org this month have a chance to win a trip with Sir Graham to release a kiwi back to the wild.
Save Kiwi Week is also supported by BNZ, Department of Conservation, Trade Me, Air NZ and Mr Vintage.
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Kiwi facts
* An average of 27 kiwi are killed by predators every week
* The kiwi population is declining by about 1400 birds every year
* In predator controlled populations, 50 to 60 per cent of chicks survive
* With no predator control, only 5 per cent of chicks reach breeding age
* A 15 per cent survival rate is needed for a sustainable population