Australia's Prime Minister is confident he will have a good working relationship with Jacinda Ardern.

However Malcolm Turnbull has been quick to stand by foreign minister Julie Bishop saying there was no need for her to apologise to our incoming Prime Minister for her previous comments that it would be "very difficult" to trust Labour.

Speaking to 3AW radio station on Friday, Turnbull said he had congratulated Ardern on her victory.

"I have got no doubt we will work together effectively, confidentially and constructively as Australian and New Zealand prime ministers have done ... for generations," he said.

"I am certainly looking forward to doing that ... I do expect to trust them."

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When asked if Bishop should apologise to Ardern, Turnbull said "no".

Australia's foreign minister Julie Bishop. Photo/Australian Broadcasting Corporation
Australia's foreign minister Julie Bishop. Photo/Australian Broadcasting Corporation

But, in August Bishop said, "should there be a change of Government, I would find it very hard to build trust with those involved in allegations designed to undermine the Government of Australia".

Her comments followed the revelation that Labour MP Chris Hipkins had been involved in outing Australia's deputy Prime Minister Barnaby Joyce as a New Zealander by descent.

Under Australian law citizens of other countries are ineligible for Parliament.

At the time, Ardern hit back at Bishop saying the foreign minister's comments were "highly regrettable" and she had contacted the Australian High Commission to register her disappointment.

At a press conference on Friday, after Winston Peters' announcement that NZ First would form a coalition with Labour, Bishop said she looked forward to working with the new government, but fell short of an apology.

Bishop said that Ardern had previously explained that Hipkins' conduct was "wrong, it was unacceptable and it should never have happened and that he shouldn't have become involved.

"And I accepted her explanation and I agree with her absolutely."

The foreign minister denied that her comments had damaged the relationship between the two countries.

She said she planned on contacting the New Zealand foreign minister when appointed and was looking forward to Ardern travelling across the ditch.

Ardern is set to become one of only 13 female heads of government in the world.

Others on the list included British Prime Minister Theresa May, Germany's Angela Merkel, Prime Minister of Poland Beata Szydlo and Prime Minister of Bangladesh Sheikh Hasina.

The countries led by the women, represent less than 7 per cent of the United Nation's 193 member states.