Mr Morrison swatted away questions about the former prime minister's book, titled The Bigger Picture, which contains various criticisms of his government.

"On this issue I will remain focused on the actual bigger picture, and that is dealing with the response to coronavirus," he told reporters in Canberra on Tuesday.

Earlier in Sydney Tony Abbott launched an impassioned defence of his former chief of staff Peta Credlin after Mr Turnbull accused the pair of sharing a bizarre dynamic.

The long-held bad blood between the two former Liberal prime ministers boiled over again after the release of Mr Turnbull's memoir.

In an interview to promote his book, Mr Turnbull said Ms Credlin had been "running the country" during the Abbott government.

"It was as though she felt, 'I've created you, you're my creation', and she felt she owned him. It was a bizarre - a truly bizarre - relationship," he told the ABC's 7.30 on Monday night.

Mr Abbott said Ms Credlin was extraordinarily capable person and an important part of his government.

"I am aware of some pretty odious comments that one of my successors made," he said.

"She was a fine thinker, a great organiser, and she was a trusted colleague. I think she deserves a great deal of credit for what she did."

Mr Turnbull says Finance Minister Mathias Cormann, who backed Peter Dutton to take over as leader, told him Mr Morrison was untrustworthy, emotional and narcissistic.

"I absolutely trust him. I've had a very strong, positive and productive relationship with Scott Morrison for a very long time," Senator Cormann told ABC Radio National.

Mr Turnbull also accused Senator Cormann of telling him to "give in to the terrorists" at the height of the leadership turmoil.

But the finance minister disputes that.

"Malcolm has presented his version of history. It differs substantially from my clear recollection of events," he said.

It didn't take long for Mr Turnbull to fire back.

"Just to refresh his memory, he said it to me on the 17th of February 2017 at 4.39pm," he told ABC Radio National.

Mr Turnbull said he overthrew Mr Abbott in 2015 because he was running a bad government.

He said his predecessor ramped up rhetoric against Muslims when terrorism was the nation's biggest domestic security issue.

"That made Australia less safe. It was profoundly dangerous," Mr Turnbull said.

After snatching the top job from Mr Abbott in 2015, Mr Turnbull was knifed in 2018, paving the way for Scott Morrison to become prime minister.

He believes right-wing Liberals and their allies in Rupert Murdoch-owned media sought to end his leadership because they couldn't control him.

"The one thing those plutocrats knew, the billionaire media proprietor knew, is that I did not belong to them," he said.

Australian Associated Press