John Key's office has released the video sent to US television host David Letterman before the Prime Minister's appearance on the show in September 2009.
The video invites Letterman to come to New Zealand, after Mr Letterman said on the show, he'd never been to New Zealand.
The Prime Minister's office says the invitation had nothing to do with Mr Key's appearance on Letterman and was not an audition.
The video was filmed in Key's Beehive office and mimics the Top 10 countdown on a subject which is a feature of every Letterman show. In the video, Key says:
Hi David. I'm John Key, Prime Minister of New Zealand. Love your show and happened to notice the interview with Nicole Kidman when you said you'd never been down to New Zealand.
So how about I give you 10 reasons to come and pay us a visit?
Number 10: We have some of the best canned ham south of the equator.
Number 9: We're still holding beard-growing contests with Peter Jackson.
Number 8: To the best of our knowledge, the Governor of Illinois hasn't tried to sell us.
Number 7: You don't have to be in bed to count sheep.
Number 6: Find out if the water really does go down the wrong way.
Number 5: Our police force is actually Xena, Warrior Princess.
Number 4: We have awesome adventure tourism, such as phone throwing with Russell
Number 3: Our scenery is nowhere near as flat as Australia's.
Number 2: We are the only country in the world where you still have a flight with the Conchords.
And the Number 1 reason, David, why you should come down to New Zealand - hip-hopping with the Hobbits.
So come on down. Pay us a visit. I'll buy you lunch.
- Newstalk ZB and staff reporter