As internal Liberal tensions continue to spill into the public arena, Mr Abbott revealed this week that he and Senator Cormann had a "man-to-man" chat after the Finance Minister in February called Mr Abbott's interventions "destructive" and "sad".

Senator Cormann is a leading conservative in cabinet and former ally of Mr Abbott.

"I don't normally talk about private conversations but look, given Tony has given his public interpretation, let me just firstly confirm that, yes, we did have a very direct conversation that day," Senator Cormann said on Sky News on Friday.

"But let me also say that I did not in any way step back from anything that I said that day."

Senator Cormann said he had previously warned Mr Abbott in private about the impact of his commentary, and noted all Coalition MPs had a duty to work together to ensure they don't "inadvertently" help Labor.

"Tony has got to be very careful that he's not seen to be helping Bill Shorten become prime minister because that would be very bad for Australia," he said.

"Some of his interventions in the past, sadly, have been somewhat destructive and were able to be interpreted as undermining our efforts to provide strong and effective and to maximise our chances of being successful at the next election."

Mr Abbott lashed out on Thursday after a leak suggested an intervention from Mr Turnbull and the Liberal Party helped save him from losing his Sydney seat.

News Corp reported on Friday that former prime minister John Howard was being considered as a potential peacemaker between warring Liberal figures.

Senator Cormann praised Mr Howard as a distinguished elder.

"As a former prime minister, I think John Howard really has defined the gold standard of how former prime ministers can best make a continuing contribution to public policy debates in our country," he said.