Minister for Social Services Dan Tehan said Mr Turnbull's leadership was not under threat.
Mr Turnbull thanked his colleagues after the votes, Ms Marino said.
Turnbull earlier declared his top position in the Liberal Party vacant at a party room meeting this morning as the battle for the Australian prime ministership got started.
Australia is due to hold a general election sometime before May next year.
"Turnbull is desperately hanging on to his leadership above and beyond everything else". Climate groups anxious that the National Energy Guarantee would not do enough to combat climate change. He later returned the favour and stormed back to power in 2013 shortly before losing the election to Tony Abbott's Liberal/National coalition. But when Hockey refused to oppose a carbon emissions trading scheme, Abbott stood at the December 1 ballot and defeated Turnbull by one vote.
Labor Prime Minister Kevin Rudd was ousted by his deputy Julia Gillard in 2010. She claimed government after 17 days of negotiation to win crossbench support.
Turnbull had attempted to see off a challenge by retreating on energy policy that was contentious among the conservative wing of his party, but his backdown was not enough.
Coincidentally, Turnbull as opposition leader in November 2009 faced a spill motion.
On Monday Turnbull had declared he had Dutton's "full support".
Mr Dutton resigned from Cabinet after the vote and will move to the backbench, triggering a ministerial reshuffle. I think he probably still is. I've spoken to nearly all the cabinet ministers from the Liberal Party.
Fellow MPs from Mr Dutton's home state of Queensland are also understood to have been encouraged to turn on Mr Turnbull.
Mr Abbott said: 'It's no way to run a government, making absolute commitments on Tuesday and breaking them on Friday'.
The Liberal party room will meet on Tuesday amid growing speculation the Home Affairs minister Peter Dutton is considering a leadership challenge.
"I've spoken to him directly and he's told me he supports Malcolm Turnbull", Pyne said.
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