Pressure is mounting on Prime Minister Tony Abbott to dump chief of staff Peta Credlin as disgruntled Liberal MPs were joined on Wednesday by conservative commentators including media baron Rupert Murdoch in expressing concerns about his office.

Former Coalition prime minister John Howard is also understood to have carried growing party-room concerns to Mr Abbott over the way his office is run under her management.

However, Mr Abbott's office rejected the concerns.

Conservative radio presenter Alan Jones was one of several normally supportive voices turning on the Prime Minister in the wake of his "captain's pick" appointment of Prince Philip as a knight.

"Here's a bloke who's made a reputation in politics for being on the wavelength of people in the street, and he just seems to have lost that touch," Mr Jones said of Mr Abbott.

Mr Murdoch, the News Corporation boss, also applied direct public pressure on Wednesday, using Twitter to demand Ms Credlin's head.

"Tough to write, but if he [Mr Abbott] won't replace top aide Peta Credlin she must do her patriotic duty and resign. More," he wrote.

"Forget fairness," he added in a subsequent tweet. "This change only way to recover team work and achieve so much possible for Australia. Leading involves cruel choices."

The comments reveal the conservative-aligned Mr Murdoch, who stays in contact with senior Liberals and regularly receives the Prime Minister and other ministers at his New York home, believes the government is no longer functioning as a team.

They also suggest Mr Murdoch has formed the view – as have a number of Liberal backbenchers – that Ms Credlin is to blame and was behind the knighthood decision even though privately she holds republican rather than monarchist sympathies.

In recent weeks Mr Murdoch is reported to have entertained Deputy Liberal leader and Foreign Minister Julie Bishop.

The day before he was elected in September 2013, Mr Abbott described Mr Murdoch as one of Australia's "home-town heroes".

"I've got a lot of time for Rupert Murdoch because, whether you like his papers or don't like his papers, he's one of the most influential Australians of all time and I think that Aussies should, we should support our home-town heroes. And that's what I think in his own way Rupert Murdoch is," he told Melbourne's Triple M radio.

The Prime Minister on Wednesday conceded the public had not reacted well to the appointment of Prince Philip as a knight but stood by the decision, while promising greater consultation for future appointments.

But the issue has become a lightning rod for serious party-room anger over the operation of the government, and the tight control of cabinet ministers by the Prime Minister's office.

Fairfax Media has been told former prime minister John Howard used a Kirribilli House lunch in December with Mr Abbott to broach growing internal resistance to Ms Credlin's role, which many MPs and ministers say is characterised by excessive control and micromanagement.

Several shocked MPs immediately cited Ms Credlin's influence in the selection of the prince for a knighthood.

Mr Murdoch is thought to be increasingly frustrated with the failure of the government in Canberra to effectively sell its reform agenda as successive opinion polls show it could yet be a one-term operation unless its ratings improve dramatically.

Mr Abbott's own judgment is also being questioned by colleagues.

Fairfax Media has learnt that Mr Abbott first raised the idea of resurrecting the knights and dames honour while he was leader of the opposition, but Ms Credlin and other advisers warned him against going through with it.

The reaction inside his office was that the idea was "f---ing stupid", according to a source.

A party source said if Mr Abbott was considering moving Ms Credlin on from his office he would inevitably face fresh accusations that he has a "problem with women".

"It would look terrible if he sacrifices a female adviser over a captain's pick," the source said.

But the source acknowledged the growing angst in government ranks at the performance of Mr Abbott's office in general and, specifically, Ms Credlin's at times "tyrannical" role at the centre of it. "Peta's list of enemies grows longer by the day and the week."

A state Liberal MP said Ms Credlin had a higher profile than most cabinet ministers, to the detriment of the federal party.

"I go to community meetings and people are talking about the Prime Minister's chief of staff," he said.

The MP said electors were telling him that Mr Abbott could only recover if he sacks Ms Credlin and demotes Joe Hockey as Treasurer in favour of Communications Minister Malcolm Turnbull.

Senior Liberals complain Ms Credlin, as an unelected official, attends cabinet meetings and have advised Mr Abbott to name a cabinet secretary from the ranks of the backbench.

Fairfax Media has also been told Mr Murdoch had expressed a view "some time ago" that Mr Abbott needed to do two key things in order to survive: replace Mr Hockey as Treasurer with Social Services Minister Scott Morrison, and get rid of Ms Credlin.

The second of those demands has now been made publicly.

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