Prime Minister Tony Abbott has sidestepped continuing speculation about a possible challenge to his leadership while making an official visit to New Zealand.

Mr Abbott was in Auckland on Saturday for security and trade talks with his counterpart John Key, and is rounding off the visit at the cricket World Cup match between the countries at Eden Park.

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The trans-Tasman visit comes amid speculation in Canberra about what could be a second spill in a month, with more Liberal MPs believed to have joined the 39 out of 102 who supported a spill motion on February 9.

Communications Minister Malcolm Turnbull is widely touted as the most likely potential challenger to Mr Abbott.

Addressing media alongside Prime Minster Key, Mr Abbott brushed off questions about a potential challenge to his leadership.

“I’m just pushing on with the job,” Mr Abbott told reporters at Government House in Auckland.

“I’m, as you would expect, undistracted and undeterred by the hyperventilating which seems to be taking place at least amongst the media.

“Every day I work for a better Australia and that’s what the party expected of me when they elected me back in 2009.”

He said he didn’t expect any opportunity to arise for a challenge.

“I’m looking forward to submitting myself to … judgment some time towards the end of next year,” Mr Abbott added.

Foreign Minister Julie Bishop, Trade Minister Andrew Robb and Assistant Treasurer Josh Frydenberg publicly backed Mr Abbott on Saturday.

Ms Bishop said she supported “the leader that the party has elected”.

“I am not aware of any attempt to bring a spill motion to challenge the leadership,” she told New Zealand’s TV3 Network.

Mr Turnbull, meanwhile, didn’t address the federal leadership question, choosing to focus instead on the coming election in NSW.

“The question the people of New South Wales have is do they want to put back into power the party of Eddie Obeid,” he said outside his Sydney home.