National Party leader Simon Bridges says he will not tolerate any of his MPs spreading rumours about politicians and their families.

Bridges said Jacinda Ardern and Clarke Gayford had his "heartfelt sympathy" after Police Commissioner Mike Bush and the Prime Minister responded to rumours and innuendo circulating about Gayford.

Ardern, who initially described the false rumours as "dirty politics", said this afternoon that she was not interested in pointing "fingers of blame" at who was behind them.

"My job is to run the country, to try and build a better future for New Zealand, this has got nothing to do with my job so I'm not going to comment on it."

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Bridges said he spoke to his caucus yesterday after hearing continued rumours about Gayford.

"This week I specifically made it clear that I will not tolerate National MPs peddling rumours or innuendo and I was specific in that being in relation to politicians, Members of Parliament and their families because these things are generally untrue," he said.

"I did not mention any specifics because I did not want to propagate it."

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Asked by the Herald if he was aware whether any of his MPs had been spreading rumours, Bridges said to the best of his knowledge none had been.

"I do not believe the National Party is involved in this in any way."

Bridges said he had not spoken to Ardern himself but he had asked his chief of staff to convey to Ardern's chief of staff yesterday that National was not involved.

Police Commissioner Mike Bush has signed off a statement from Police National Headquarters saying: "While in general we do not respond to enquiries which seek to confirm if individuals are under police investigation, on this occasion we can say that Mr Gayford is not and has not been the subject of any police inquiry, nor has he been charged in relation to any matter."

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Bridges said he had twice addressed caucus to set expectations about dealing with politicians' families.

"My heartfelt sympathy to the Prime Minister and Clarke Gayford. It is entirely unacceptable and politicians families should be left out of politics."

Bridges said if "dirty politics" was involved, it was not from the National Party.

"If it is, I entirely strongly reject that.

"I made my expectations to my Members of Parliament, when I heard and kept hearing these rumours, very clear."

Ardern issued a statement saying: "I won't comment on dirty politics. It's just not what I'm here for."

Stopping briefly on her way into a parliamentary event today to speak to media, the Prime Minister said she had nothing to add.

"This is not why I'm here, this is not why I'm in politics, and I've got a job to do and I'm going to do it."

She did not respond to a question about whether she thought it was dirty politics.

Ardern was accompanied by her chief press secretary, Mike Jaspers, and another press secretary, Leah Haines. She was heading into the Grand Hall to present the Prime Minister's top scholar award.

A lawyer for Gayford has also written to some media warning that the unidentified rumours are defamatory - and publishing the allegations "is actionable."

The letter is signed by Linda Clark, a former TVNZ political editor, who now works as a lawyer at Kensington Swan.

"The allegations (which the NZ Herald did not publish) are untrue and defamatory. The story included a statement from the NZ Police that Mr Gayford is not and has not been the subject of any police inquiry," Clark's letter says.

"We draw your attention to this for the purpose of putting you on notice that any publication of the substance of the allegations regarding Mr Gayford will result in proceedings being filed immediately."