Conservative media baron Rupert Murdoch has called on Tony Abbott to show leadership and make the "cruel choice" to sack his controversial chief of staff - and if the Prime Minister won't act, Peta Credlin should resign.

Mr Murdoch's intervention is the second since Mr Abbott's decision to honour Prince Philip with an Australian knighthood on Australia Day - a choice that has also prompted serious chatter amongst Liberal MPs about the Mr Abbott's leadership.

Rupert Murdoch took to Twitter on Wednesday: "Tough to write, but if [Tony Abbott] won't replace top aide Peta Credlin she must do her patriotic duty and resign."

Just days after Mr Abbott dismissed social media as "electronic graffiti", Mr Murdoch weighed into the debate via Twitter and urged the Prime Minister to "forget fairness" and focus on "team work".

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