Fresh speculation around a challenge to Tony Abbott's leadership threatens to overshadow his first official visit to New Zealand. It now looks possible that his first official could be his last.

New reports from Australia suggest that former leader Malcolm Turnbull has enough support to win a leadership spill and it is just a matter of when, not if, he is challenged.

READ MORE: Margie Abbott, Tony Abbott's down-to-earth Kiwi wife

A press conference in Auckland this afternoon held by Foreign Minister Murray McCully and Australian Foreign Minister Julie Bishop was dominated by questions about the Liberal Party leadership from Australian and New Zealand reporters.

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Ms Bishop did nothing to dispel speculation that she, too, could put her hat into the ring in a leadership vote.

In the last vote, on February 9, on whether there should be a leadership vote, Ms Bishop was seen as a potential contender.

Ms Bishop was asked if she would like to be the next Prime Minister of Australia she said the role was occupied by Mr Abbott and the last leadership spill motion did not succeed.

"These questions are all hypothetical speculation."

She said speculation was not helpful.

"I'm getting on with my job as Foreign Minister. The Prime Minister is getting on with his job as Prime Minister and we urge our colleagues to focus on the interests and concerns of the Australian people."

Mr Abbott has been trying to secure his position on the concept that he was elected Prime Minister by the Australian people and that it should be up to them, not the party room, to change leaders.

When Ms Bishop was asked if the job of the public or the party room, she said:

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"It is self evident that the individual member of the party room are able to elect the leader and the deputy leader of the Liberal Party and that has always been the case. I imagine that will continue to be the case."

She said she and Mr McCully had talked about regional security and New Zealand's work on the Security Council.

She was asked why Mr Abbott had delayed an expected announcement in the increase of Australian troops deployed to Iraq from the 600 currently there - virtually announced on Tuesday by Prime Minister John Key when he announced New Zealand's deployment of 143 personnel.

But she would not confirm it was even imminent.

"Well I'm sorry that the Prime Minister of Australia hasn't made announcements according to your expectations," she said.

"Australia already has a considerable presence there and as the Prime Minister has said, we will continue to review the composition of our presence and what more we can do to assist."
Australia was there at the invitation and consent of the Iraqi Government.

"It is not a matter of Australia making unilateral decisions as to how it wants to deal with its defence forces in Iraq."

After a Maori welcome at Government House, Mr Abbott is due to lay a wreath at the Auckland War Memorial before attending a transtasman leadership forum.

Formal talks will be held tomorrow before Mr Abbott and Prime Minister John Key will go the NZ vs Australia cricket match.

Asked by an Australian reporter if Australia would consider backing former New Zealand Prime Minister Helen Clark to become Secretary General of the United Nations, over a possible Australian candidate, Ms Bishop said the question was hypothetical.

"If an Australian were to indicate that they wanted to be Secretary General of the United Nations we would consider that at the time.

"I understand that there is a lot of interest in Helen Clark taking on the role but she has not formally approached Australia for support."

It is thought that former Australian Kevin Rudd has canvassed the idea of standing.