National Party leader Simon Bridges has warned Winston Peters against making comments about the leadership crisis in Australia's on his visit there today - as he did recently about upheavals in British politics.

But Bridges said he himself was not similarly constrained as Opposition leader and believed that sitting Prime Minister Malcolm Turnbull "deserved to win the next election - but disunity kills."

Peters' arrival coincides with another bid to unseat a sitting Australian Prime Minister, with hardline minister Peter Dutton losing 35 votes to 48 votes, before resigning his Home Affairs portfolio.

Bridges said Peters had got it wrong when he commented on Boris Johnson's resignation as British Home Secretary and he and Prime Minister Jacinda Ardern should resist the temptation to comment on Canberra. The Australians should be given space.

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"Having said that, what I can say as Opposition leader is a little less restrained than the Prime Minister or Deputy Prime Minister.

"It is a remarkable turn of events. For the Liberal Party, the worry is that they will shoot their foot off, possibly their whole leg.

"They have got an economy that is firing and yet disunity really hurts. You'd think they have to be very careful about handing an election in a few months' time to the other side through more of what we've seen in the past 24 hours."

But sometimes that was not enough and people could take that for granted, Bridges said. If Dutton ousts Turnbull, that will be four consecutive prime ministers who will be rolled.

Canberra is alive with speculation that Dutton's respectable muster means another fresh challenge in the coming weeks and the possibility of a new prime minister who has sparred openly with New Zealand in the past, including Peters.

Dutton has been critical of New Zealand's offer to take asylum seekers from Australia's offshore processing centres and suggested it has not pulled its weight in stopping people smugglers.

And he has been largely unmoved by New Zealand's pleas to stop deporting New Zealand-born criminals who have spent most of their lives in Australia.

Ardern told reporters yesterday that whoever was the Prime Minister, New Zealand would not change the issues it took up with Australia.

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And regardless of who replaced Dutton in his portfolios, "we will be looking to have that same constructive relationship and we will continue to raise the same issues as we always have."

"Our relationship continues regardless of the political environment."

She would not speculate on what policy changes might take place with Dutton gone from Home Affairs.

Sky News' New Zealand Bureau Chief James O'Doherty said he did not expect any shift in the policies of offshore processing or deportation of criminals.

The deportation issue had been quite successful in Australia.

"The voters don't care about it as much as Kiwis do for obvious reasons. Even when a new Home Affairs Minister is appointed I wouldn't expect anything to change then either."

O'Doherty did not foresee any change in deportations or the offshore processing policies if Dutton became Prime Minister.

"The Australian Government already has a fairly hardline stance on both of those issues."

But how Dutton would work with Jacinda Ardern would be interesting if Turnbull was mortally wounded.

"At the end of the day he had 35 people vote against him in his own party room. How he can stand up and say he enjoys the confidence of his party is very questionable."

Dutton was not ruling out a further challenge and it did seem as though it would come to a head in the coming days or weeks.

Peters is meeting Foreign Minister Julie Bishop and speaking to the National Press Club in Canberra about the transTasman relationship.