It will be pretty much business as usual after the change of leadership in Australia , Prime Minister John Key says.
Mr Key said he had spoken to Malcolm Turnbull earlier this morning.
In a dramatic ballot of Liberal Party members last night, Mr Turnbull received 54 votes to Mr Abbott's 44.
After his victory last night, Mr Turnbull outlined his plans for leadership that "persuaded" rather than "lectured", and pointed to Mr Key as a leader to emulate.
"To be a successful leader in 2015 or at any time you have to be able to bring people with you by respecting their intelligence in the way you explain," said Mr Turnbull. "New Zealand prime minister John Key is the model for explaining complex issues and making the case for change, achieving significant economic reforms."
Mr Key said he had spoken to his counterpart and the outgoing prime minster.
"I said we looked forward to a strong and constructive working relationship with Australia, as we've enjoyed for many years, and wished him all the very, very best.
"I also sent a text to Tony Abbott last night, I've developed a good working relationship with Tony over the last couple of years, but politics is a brutal business as we all know."
Mr Key was asked about Mr Turnbull's comment that he would like to emulate his political style and way of communicating.
"Yeah, he made those comments to me on the phone, well, let's wait and see."
He said he thought it was a genuine sentiment from Mr Turnbull.
"He genuinely thinks that New Zealand's had stable leadership over a period of time and has delivered good economic results, and that is flattering, but equally we understand this has been a very tumultuous time in Australia.
Mr Key said it appeared Mr Turnbull was quite different to his predecessor, Mr Abbot, and more moderate.
"So if you sort of consider me to be very much a moderate, in the centre of the National Party, I think that's where you'd find Malcolm Turnbull, he's very much in the centre of the Liberal Party - he'll have more progressive views I think on things like gay marriage for instance."
Mr Key also noted Mr Turnbull, like himself, comes from an investment banking background so comes with "strong economic credentials."
He said Australia would now be looking for stability.
"I think they've had about as, the only country we can see in the Pacific, that's had more change in this short period of time is Vanuatu."
And he said he did not believe there would be a dramatic change in the trans-Tasman relationship.
"In fact, you know, when Julia Gillard was prime minister, she was very engaged with New Zealand, Kevin Rudd a little less so to be blunt, but Tony was very focussed on New Zealand and I think Malcolm will be very focussed on New Zealand so in that regard not a lot has really changed.
"I mean the face changes, but actually every Australian prime minister I've met always thinks that New Zealand is really critical in terms of that Australasian, ANZAC bond."
And what was Mr Key's message to Mr Turnbull?
"The same advice I'd give to any leader which is just trust your instincts.
'The camera never lies, so people can tell whether you're speaking from the heart and whether you actually believe what you're saying, if you are and you do, most people will give you the benefit of the doubt.
"In my experience the public has quite a low level of expectations in their government and their prime ministers and they just want them to get on with it and do the job. And if you can do that in a way that lets them get on and live their lives, they'll give you quite a lot of leeway."
Labour leader Andrew Little also had a response to Mr Turnbull's comments about wanting to emulate John Key.
"I pity Australia if that's the case."
"We've got a prime minister that's presided over seven deficits. a growing public debt, and an economy that doesn't have much to show for seven years of a National government, if that's Malcolm Turnbull's ambitions then I pity Australia."
More broadly, Mr Little said there were deep-seated problems in Australian politics.
"I don't know exactly what it is apart from something in Canberra's water. But it is an unusual turn of events for a large, developed country like Australia to have such a rapid change in prime ministers, and no elected prime ministers serving out their full parliamentary terms."
Mr Little said the nature of politics means all political careers end in failure.
"It is a tough business, so you know they all have a go at each other, but I think there is something more disturbing in Australia, there is a level of instability within the political establishment that is not healthy for Australia, and for New Zealand that relies on trade with Australia to a huge extent."