Tony Abbott has refused to buy into explosive new claims that his colleagues believed he was having an affair with his chief-of-staff, Peta Credlin.

A new book by News Corp columnist and former Coalition staffer Niki Savva contains fresh claims that a number of government frontbenchers warned him that his job was under threat unless he sacked the divisive Ms Credlin.

Confronted about the claims at Sydney Airport on Saturday, Mr Abbott said he did not want to "rake over old coals".

"I know some people do want to rake over old coals but I don't," he told reporters. "I think the focus has to be on getting the Turnbull government elected."

In The Road to Ruin: How Tony Abbott and Peta Credlin Destroyed Their Own Government, Savva writes that Abbott loyalist and conservative NSW senator Concetta Fierravanti-Wells sounded the warning in February 2015.

"Politics is about perceptions," Senator Fierravanti-Wells is quoted as telling Mr Abbott. "Rightly or wrongly, the perception is that you are sleeping with your chief of staff. That's the perception, and you need to deal with it.

"I am here because I care about you, and I care about your family, and I feel I need to tell you the truth, the brutal truth. This is what your colleagues really think."

Mr Abbott denied the rumours and refused to sack Ms Credlin. Senator Fierravanti-Wells has since publicly confirmed the accuracy of Savva's account.

Turnbull government minister Christopher Pyne sought to downplay the book's revelations.

"I have to say I thought it was a bit of a fizzer to be honest. It was certainly pretty benign," he told Sky News.

"If that's all that Niki Savva has in her book, I don't think that's going to cause too many ripples. There wasn't anything particularly new in it."

Labor frontbencher Richard Marles said there was interest in a change of prime minister.

"But serious journalism is about the accurate historical account. It is not about being a gossip columnist," he said.

Separate details of the book's contents published by veteran broadcaster Laurie Oakes detail how Ms Credlin fed the then prime minister food from her fork at an Italian restaurant in Melbourne. She then rested her head on his shoulder and complained of being tired.

It was this sort of behaviour that sparked endless gossip in Canberra about the dynamic of the prime minister's dependence on his staffer.

Since their fall from government, Mr Abbott has asked Prime Minister Malcolm Turnbull to appoint Ms Credlin Sex Discrimination Commissioner and to make Mr Loughnane Australia's Ambassador to the Vatican – both requests the new Prime Minister has declined.

- with Latika Bourke