to oust the Prime Minister.
"We strongly support the Turnbull leadership of course and we want to see the Coalition government successfully re-elected early next year when the election is due".
The coalition has lost 38 successive Newspolls to Labor, eight more than Tony Abbott's record.
Mr Turnbull had brought on the vote himself in a bid to resolve speculation that his leadership was under threat.
The leadership challenge is the latest development in what has been a turbulent period for Australian politics.
Peter Dutton received 35 votes, a significant chunk he could build on going forward.
The only question appears to be whether Mr Dutton will strike immediately or wait until parliament returns on September 10.
Choosing to back down on the emissions legislation shows that Mr Turnbull wants to avoid testing his support in a parliamentary vote.
He was criticised by Liberal Warren Entsch, who reportedly "got stuck into" Mr Abbott in the joint party room meeting.
Dutton said he respected the outcome of the ballot and fully supported Turnbull.
Frydenberg said Cabinet ministers on Monday night expressed their support for Turnbull, including Dutton, who was a staunch ally of Abbott.
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".
The position of Deputy Leader was also spilled and Julie Bishop was re-elected unopposed.
"Voters will do what they always do they react very badly to internal tensions, to disunity", Mr. Economou said.
Mr. Frydenberg said voters were exhausted of governments repeatedly changing their prime ministers.
To stave off a revolt, Turnbull has backed down on a plan to legislate Australia's Paris Agreement commitment to cut emissions by at least 26 percent below 2005 levels by 2030.
The concession avoided the most conservative government lawmakers voting against the legislation in Parliament, openly undermining his authority.
Mr Dutton's supporters circulated a letter on Wednesday night calling for the party room to meet.
Australian Prime Minister Malcolm Turnbull has survived a challenge to his leadership by a senior government colleague. "They hate it when we are talking about each other".
"Playing footy against a lot of children is pretty weird", one user said, while another added: "Peter likes football, long walks on the beach and torturing refugee children".
Fellow MPs from Mr Dutton's home state of Queensland are also understood to have been encouraged to turn on Mr Turnbull. Australia has seen five different leaders since 2009.
He dodged giving a direct answer every time. "My job is to make sure I can prosecute the sort of messages I spoke about and that is the only thing I am focussed on", he said.
Dutton refused to rule out another tilt at the top job, saying he made his move in the belief that he had the best chance of steering the party to an election victory. "Will push to change those numbers?" "I'm very proud of the fact that I got children out of detention - we've moved now nearly 400 people off Manus and Nauru that Labor put there, and that is a significant achievement".
Now effectively neutered and unlikely to proceed, the NEG will become a millstone for Turnbull as he tries to rally his diminishing support base.