The Prime Minister this morning dealt “head on” with internal criticism against Ms Credlin, calling on his colleagues to “take a long, hard look at themselves with some of these criticisms”.

“If people have a problem with my office, obviously they can tell me because what my office does is what I ask my office to do,” Mr Abbott told ABC News 24.

“The point I want to make is first of all this is the same office which ran a very effective opposition, it’s the same office which has got an enormous amount done this year, sometimes under very difficult circumstances.

“The other point I make: do you really think … that my Chief of Staff would be under this kind of criticism if her name was P-E-T-E-R as opposed to P-E-T-A?”

Mr Abbott, when asked if that was directed at his Coalition colleagues, said: “I think people need to take a long, hard look at themselves with some of these criticisms”

There have been reports — never comprehensively denied — that Ms Bishop “went bananas” when told the Prime Minister’s office refused her request to represent Australia at UN climate talks in Peru. She reportedly took her case to cabinet and Mr Abbott acceded with the requirement that Trade Minister Andrew Robb also go as her “chaperone”.

When Julia Gillard in 2012 claimed she was treated differently to her male predecessors, Ms Bishop said: “If she plays the gender card, she is wallowing in self-pity over her own performance (and) that’s what it appeared to me.”

There has been speculation that Ms Credlin might leave Mr Abbott’s office to campaign for her own seat in parliament, although she has denied any intention “at this time”.

Social Services Minister Kevin Andrews described Ms Credlin as “integral” to the government and urged his colleagues to “stick to policies and programmes” rather than be “diverted by personalities”.

Labor’s Chris Bowen said Mr Abbott’s reprimand of his cabinet colleagues underscored “dysfunction and chaos” in the government.

“Mr Abbott has previously said when he was leader of the opposition that the gender card shouldn’t be played and that all criticism of then prime minister Gillard was based on performance; he seems to have applied a different test when it comes to the criticism of his chief of staff by his own cabinet members,” the opposition treasury spokesman said.

Mr Bowen said opposition frontbenchers had no public criticism to make of Ms Credlin.

“The speculation you’re reading is very clearly coming from within the government as a sign of the dysfunction and chaos in Mr Abbott’s administration,” he said.