By Agence France-Presse
Former home affairs minister Peter Dutton, an ex-police officer and right-winger, has been the stalking horse seeking to unseat Turnbull after a party backlash against his more moderate approach to politics.
Turnbull survived one attempt to knife him on Tuesday, winning a party room vote 48-35, but since then ministers have been defecting and a second leadership challenge is likely at noon (0200 GMT) Friday.
Dutton needs to prove he has majority backing, or 43 signatures from within the party's parliamentary group -- a requirement for him to force a second crack at the top job ahead of national elections due by mid-2019.
Reports on Friday said at least 40 lawmakers were onboard for a leadership change.
Turnbull, who accused Dutton and his supporters of bullying and intimidation, on Thursday said he would not contest a second leadership challenge and leave parliament, although he did not put a timetable on when he would go.
If he moves out of politics, it would spark a by-election for his Sydney seat, threatening the government's one-seat parliamentary majority.
Even if Dutton gets the numbers for a challenge, there is no guarantee he will assume the top job after foreign minister Julie Bishop and treasurer Scott Morrison, both Turnbull allies, threw their hats in the ring.
During a three-way vote, whoever comes last in the first round will be eliminated with a second round taking place to decide who becomes leader.
Defence industry Minister Christopher Pyne, a Turnbull ally, refused to say who he would be backing and hit out at elements inside his party.
"I think some people should have considered the greater good of the people of Australia, and the government, rather than their own self-interest and ambition," he said.
Owe you an apology
The unrest is the latest chapter in a turbulent decade for Australian politics, with no leader managing to serve out a full term since former Prime Minister John Howard lost the 2007 election.
If a new leader takes office Friday, it will be the seventh prime minister in 11 years in a remarkable revolving door at Canberra's parliament house.
Complicating matters, Dutton was referred to the solicitor-general over his eligibility to sit in parliament due to family financial interests in childcare centres that receive government subsidies -- a possible breach of constitutional rules.
The nation's top lawyer has since cleared Dutton to continue in parliament, reports said Friday.
If he succeeds in taking the top job, Dutton will push Australian politics further to the right with a shift in several policies.
He has made clear already that he would slash the migrant intake to counter population pressures and has not ruled out withdrawing Australia from the Paris climate agreement.
The move to oust Turnbull was sparked by his plans on Monday to embed carbon emissions targets in law.
Coupled with the government long trailing the opposition Labor party in opinion polls, the move sparked a revolt that quickly spiralled into calls for his head.
One minister was so disillusioned with the push to oust Turnbull that he took to Twitter to apologise to the Australian people.
"Australia. We owe you an apology. I'm sorry. You deserve better than many of the things our Federal Parliament has served up to you for the past 10 years," wrote Nationals MP Darren Chester, whose party is in a coalition with the Liberals.