"I can understand why they take it seriously over there because she is in a government with a majority of one," he said.
"I can see why they reacted in the way they did, but I don't think it should be a measure of the relationship. And I would imagine that as emotions have cooled we will be able to have the relationship on an even keel.
"This will pass ... cooler heads now will get the issues resolved."
As the fall-out from Labour MP Chris Hipkins involvement in the citizenship saga surrounding Australia's Deputy Prime Minister Barnaby Joyce continues, Bishop appeared on Sky News Australia and was repeatedly asked if her extraordinary comments went too far.
"Not at all," she said. "After I said that the New Zealand Labour leader came out and conceded that the conduct was wrong, that it was unacceptable, that it should never have happened."
Asked by host Kieran Gilbert if she accepted Ardern's comments and would now move on, Bishop said "I take her at her word".
Gilbert suggested Bishop had made her comments because New Zealand was a smaller country, telling Bishop she wouldn't have made the same comments if an MP was involved in China, Indonesia, or India.
"I reject that," Bishop said.
"I reject the fact it seems to be acceptable conduct in the minds of the commentariat here for the shadow minister for foreign affairs to use her office to set-up a Labour MP in New Zealand to ask questions in the New Zealand Parliament."
Ardern called in High Commissioner Peter Woolcott last night after Bishop said she could not trust a future Labour Government if it had colluded with Australia's Labor Party to try to undermine the Government by uncovering the fact Joyce was a New Zealand citizen.
Ardern said she told Woolcott MP Chris Hipkins' actions were inappropriate in asking questions that related to the issue of citizenship by descent after a conversation with an Australian Labor Party staffer, but stopped short of apologising.
Marcus Ganley, Australian Senator Penny Wong's chief of staff, was the Australian Labor Party staffer who spoke to Hipkins - a conversation Hipkins said prompted him to ask questions of Internal Affairs Minister Peter Dunne on the legal citizenship status of an Australian born to a New Zealand father.
The question of New Zealand citizenship of Australian ministers was raised again this week after it was revealed Deputy PM Barnaby Joyce was a New Zealand citizen. Yesterday Joyce told Parliament he had renounced his citizenship.
Ganley was an adviser to former PM Clark and former Finance Minister Cullen during the Labour Government until 2008. He then advised Phil Goff as Opposition Leader.
Hipkins has denied knowing there were questions about Joyce's citizenship, saying he asked the questions of Dunne to clear up the law.
Wong told the Australian Senate today questions about Joyce's citizenship had been asked by the media for some time, including in July.
"The story became public as a result of media inquiries.
"At no stage did my staff member request that questions be placed on notice in the New Zealand Parliament. End of story.
"Second, I did not know, nor did my staff member, that the New Zealand Labour Party had placed those questions on notice, until the story had broken. He did not know, and neither did I, until Monday."
Internal Affairs Minister Peter Dunne said it was a "silly spat" and described Australia Foreign Minister Julie Bishop's comments as "unwise."
"This is a fraught time for them as the consequences are pretty dramatic."
Questions remain about whether Labour MP Chris Hipkins' questions were a factor in officials looking into Joyce's situation.
When Joyce revealed he was a New Zealand citizen in Australia's Parliament on Monday, he referred to New Zealand officials looking into it after inquiries by the NZ Labour Party.
Dunne remained adamant it was a journalist which prompted the inquiries, and said he did not know how Joyce had known of Hipkin's questions or any involvement by the Labour Party.
"There's quite a long trail about what was known at what time."
Dunne's version of events conflicts with Foreign Affairs Minister Gerry Brownlee , who has said Hipkins' questions were a prompt for the DIA investigating.
Hipkins lodged his questions two days after an Australian journalist asked about the same scenario of an Australian with a New Zealander father.
It is understood when the Ministry of Foreign Affairs was first briefed by Internal Affairs, both the journalist's and Hipkin's questions were referred to.
An Australian journalist asked questions about the legal status of an Australian with a father born in New Zealand last Monday and Hipkins lodged his questions last Wednesday, August 9.
On August 10 officials looked at it and on the Friday advised the Ministry of Foreign Affairs it was likely Joyce was a citizen so the High Commission could handle it.
The High Commissioner Chris Seed told Joyce, who revealed it publicly on the Monday in Parliament.