With Turnbull, a social liberal who supports fighting climate change, struggling to unite the party, local media reported Home Affairs minister Peter Dutton was considering a leadership challenge.
The change follows a revolt by conservative members of parliament against Turnbull's energy policy, and some Liberals have threatened to cross the party line.
A report in The Australian suggests Mr Turnbull had lost confidence of nine Liberal cabinet ministers - half of the Liberal contingent.
The stunning retreat emerged as the energy issue threatened to turn into a crisis for Turnbull's leadership, and the government worked on measures to reduce power prices to meet the demands of Coalition dissidents.
A defiant prime minister is holding onto his leadership with support from two key lieutenants as Mr Dutton is pushing to challenge him again.
However, facing backlash from his Coalition government and the threat of a leadership challenge, Turnbull tried to appease critics Friday by proposing setting emissions reduction targets by regulation instead of legislation.
"But I have most enjoy being minister for home affairs because of the people who work within those agencies and the incredibly important work that they support".
Abbott had signed Australia into the Paris Agreement while in office, but later withdrew his support after losing a leadership challenge to Turnbull.
Turnbull said he asked Dutton to stay in his ministerial post but Dutton declined.
Cormann, a fellow conservative who is close to Dutton and said they had had four walks this week at 5.30 am, told Sky, : "We are both very committed to the success of the Turnbull Government and to winning the next election.
His position remains in jeopardy despite surviving Dutton's challenge, stoking expectations of further political instability in a country that has seen six different leaders since 2009.
Another said the Prime Minister's condition was "terminal".
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"[Foreign Minister] Julie Bishop was the one person who nominated for that role and she's the Deputy Leader of the Liberal Party".
Turnbull ruled out any retribution against ministers suspected of supporting Dutton and said he had invited Dutton to remain in the senior security portfolio.
Federal Gold Coast MPs have overwhelmingly backed Peter Dutton over Malcolm Turnbull in a dramatic day in Canberra. I have invited him to continue in that office.
That's a question I think you'll have to address to him.
Backers of likely leadership challenger Peter Dutton, the conservatives' standard-bearer, insist his support levels are building rapidly.
Yet with Australia now enjoying a record 27th straight year of economic expansion, with low unemployment, low crime and high personal wealth, why has politics Down Under become so turbulent?
"I believe strongly that we can win the election if we get the policies and the message right about lowering electricity prices, about making sure that we can do more on infrastructure and in particular around the migration program, until the infrastructure can catch up in our capital cities", he said. "They don't like us being focused on ourselves", he said.
Mr Dutton was just seven votes short of being Australia's Prime Minister.
Former Liberal leader and Australian Foreign Minister Alexander Downer has blamed "hysterical" political commentary for the sudden bout of Italian-style turmoil.
I have seen leadership challenges before and this was a resounding vote of support in the leadership team.
"I don't believe so, and the reason for that is we're getting on with the job and just announced another big change in terms of going forward with the ACCC", Mr Morrison responded.
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